Triple or Multiple Integral dx,dy,dz-Video
Triple Integral calculator example dx dy dz
Full Video Transcript
Hello again everybody this is Tom from everystepcalculus.com everystepphysics.com. This time calculus triple integral with the order of integration dx dy dz. Let’s do an index8() to get to my menu.
We’re at triple integrals already XYZ. And we’re going to enter the function alpha first before you enter anything in these entry lines, remember that. Alpha x squared plus y squared plus Z squared.
It always asks if it’s ok so that you can change it in case you made a mistake. And we’re going to want to do number 1 dx dy dz. There’s the region. So our limits of integration alpha 0 alpha 1 okay? Alpha minus 2 alpha 4 okay? Alpha 2, alpha 5.
Again here they are , notice that you’re going to do dx dy dz you’re going to do with respect to X first. Integrate this with respect to x, then y, then z. Here’s the x limits here’s the y limits, here’s the z limits.
So with respect to X here’s the answer here and then over 1 over 0 at x equals 1 this is the answer here. You put…remember to put parentheses around these instead I have to put quotation because of the program but i’d rather have parentheses. I want you to put parentheses around these quotation marks because you’re substituting something in for a variable that’s the way you do it in math.
And then the upper minus the lower so here’s the answer for that respect to x. Now we’re going to integrate that and then over these limits. So the integration of this with respect to y is this right here. And then over 4 minus 2 at 4 ,this is the answer. At minus 2 this is the answer.
Now upper- lower and we have this right here now we’re going to integrate that. dz with respect to z and over 5 and 2 here’s the integral of that. And now a limits at Z equals 5 here they are here’s the is the answer 380. And C equals 2 here’s the answer 68.
Now upper- lower answers is 312 cubic units. Pretty neat huh try that by memory try to do that by memory on a test very difficult, let alone a week after you get out of calculus, you won’t remember this forever . Have a good one!
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Triple Integral calculator example #1
Double Integral Limits of Integration-Video
Double Integral Limits of Integration-Video
Raw Transcript
Hello, Tom from everystepcalculus.com and everystepphysics.com. Double Integral today. On this video. Um, so let’s do it. Index 8 to get to my menu. We’re going to scroll down to the D section. You can use the second and then the arrow to go, you know, quicker. Screen by screen. But there is Double Integral right there. And we’re going to enter our function and we’re going to press Alpha first before you enter anything into these entry lines, here. Alpha X times Y plus X squared times Y cubed. I always show you what you’ve entered, you can change it if you want. And now we have to decide whether we want to do it from dy, dx or dx, dy, that’s the order of integration. We’re going to go with number 2, dy, dx. And here we have if dx is on the outside then it’s on the outside here and this is on the inside therefore the ay by is, the limits are involved with the dy inside. So remember that. dx is on the outside therefore these go with the dx. dy is on the inside the limits of integration go from ay to by. So let’s enter those now. And there’s the region. Just like this in notation. So we’re going to do Alpha 1 to Alpha 3. Say it’s okay. We’re going to do Alpha 0 to Alpha 2. I say that’ okay. And there’s out integral right there. We have the function inside here, dy dx. And here’s the x on the outside and the limits of integration 0 to 2 on the inside. So with respect to Y, we integrate with respect to Y. Here’s the answer x squared times y to the fourth over 4 plus x times y squared over 2. And we’re going to do that over the 0 on the 2 limits. So at x equals 2, you add. You see quotation marks here but I can’t, I would like to put parentheses in for those because we’re substituting y equals 2 for all the y’s in this function, here. So you’re going to have to put the parentheses in every time you see quotation marks, put parentheses, okay. And then 4 squared plus 2 x and that’s what that equals and then y equals 0 and then here’s the 0’s in for Y and that equals 0. And 4 x squared plus 2x minus. The upper limit minus the lower limit is 4x squared plus 2 times x. Now we integrate that with respect to the limits 1 and 3 with respect to x. So we integrate that. Here’s the answer here. 4x cubed divided by 3 x squared over 1 in 3. The limits. And x equals 3 here, we’re substituting 3 in for all the x’s equals 45. And x equals 1. You substitute 1 for all the x’s, you get 7/3. So upper minus lower 45 minus 7/3 equals the are is 42.7 square units. Remember the an integral always gives\you the area under a curve. And so I always put square units in there. Alright, have a good one.
Calculus Q & A
Question:
An email from a Calculus student:
Hi Tom,
First, I want to sincerely thank you for the support of your wonderful programs. You’ve inspired a knowledge of calculus that my prof cannot.
I’ve got a problem to find the extremas of an exponential function over a given closed interval but don’t know which program to use. Here’s the problems:
f(x) = (3x-1)e^(-x), on the interval [0, 2]
and
f(x) = (ln (x+1))/(x+1), on the interval [0, 2]
any advice would be greatly appreciated!
Thanks!
Answer:
In short you enter the function into my “graph by hand” menu program.
Calculus to me is like teaching you how to multiply through the 9’s and then make a student take three semesters siting a million areas of the usage of multiplication.
Calculus finds two things, the derivative finds the “slope of a line”, that’s it!!! and the integral finds the “area” under a smooth curve (x^2,x^3,x^4,x^5 etc and sin(x) and cos(x) (called a sine wave) as you graph those on an x y graph, and only finds the area, if you give that integral a range, called a “definite integral” an indefinite integral finds nothing.
To me calculus is the Sudoku of math, the study of cross word problems. Something to do while waiting for a plane to Phoenix. In calculus they don’t say “rose” (ya know the flower) they say “hibiscus mutabilis” they constantly make easy things into extremely hard things. Linear approximation is a prime example, as well as related rates.
That said, “extrema” “max and mins” of a function is the absolute or maximum high points or low points as you look at a graph of a function. If you graph -x^2 (minus) this is a smooth mountain, extrema is standing at the top. The opposite is true of x^2 (positive) this is a smooth valley, if you graph it, and you are under that valley, touching it with your finger at the lowest point.
That said, it just so happens that when the slope of line is “horizontal” it has a slope of zero, and if you set that horizontal line on top of the mountain it will touch at only one point (tangent) and that point will be the highest possible point on that mountain. So calculus take the first derivative of a function (slope of a line), sets it equal to zero and then solves for the x values. It then puts those x values back into the origininal function, and when solved, finds the “y” value. That point (x,y) is the maximum or extrema of that graphed function. Those x values are called “critical numbers” because they lie on the x axis. They become “critical points” when you plug them into the original function and solve for “y”.
Now to me in your first example, given what I’ve just taught you, They say “over an interval” and then give you the inteval [0,2] (Notice the brackets which indicate an interval where parenthesis would indicate a point (x,y) in math — There is only one critical point (no interval) where the hoizontal line would touch the graph (tangent), so I guess this “over the interval” is to throw you off, or check whether your understanding is as good as mine.
My graph program will do all this for you, but in the first example if written properly (get used to doing this) would look like this: (3*x-1)*e^(-x). Notice the times sign in front of the “e” that tells you product rule to find the derivative. In the second example quotient rule would be used to find the derivative.
Thanks, for the kudos, Tom
Solving Definite and Indefinite Integrals – Q&A
Dear Tom,
I would like to know if your program also solves integrals consisting only of symbols like x, a or b in both definite and indefinite matters?
Example:
or
Would solving does definite integrals be possible using your programs showing the solution process step by step?
Kind regards,
Ben
Answer
The first integral, sounds like your professor didn’t teach you, so you will want my programs to teach you or me to teach you. A common endeavor in my experience. When you see the da that’s “with respect to” in other words, you are integrating that integral with respect to “a”. In my programs you’d change all the “a’s” to x”s.
Now could you solve the integral if it looked like:
x x
∫ (1/x)dx or ∫ ( 1/[(c+b)-(k+x)] ) dx
o o
Now these would never appear on a test unless your professor demonstrated them on the black board, so they are either homework or experimenting off the internet. Both integrals are definite integrals because they show a range to integrate over. When you solve the integrals you have the area under that functions curve. That’s all integrals do is solve area under curves. You can graph 1/x on your calculator and you can see what the first integrals function looks like. Now, anytime you see a function without an exponent in the denominator, it is a natural log answer. The reason is is that you can’t integrate term with a division sign.
In this case the x has an exponent of 1 ( x^1), you always have to move the denominator to the numerator to eliminate the division sign before you can integrate. If you move the x^1 to the numerator to eliminate the division sign it becomes x^(-1) so when you do the integration process which is always add 1 to the exponent and divide the term by that answer, However when you add 1 to a -1 you get zero, and any term to the zero exponent = 1, so that’s why the natural log comes in. In the first integral above = ln(x), then you can enter the ranges for x that you are given, do the top range first and subtract the bottom range to get the answer (area under the curve of the function). The second integral above you’d break it into two integrals ∫[1/(c+b)] dx which equals x/(c+b) and then the second term 1/[(k+x)]dx which equals ln(k+x).
3 Calculus Questions Solved by TI-89
I’m really trying to figure out how to use your program with a couple different problem examples:
“Find the following derivatives of f(x). Do not leave any negative exponents”
1. F(x)= 4^x-ln(2x^2-x)
What program can I use to solve this?
another is f(x)=2csc(x)+5arccos(x)
This is fundamental to calculus and you must start to learn it or know it.
Notice the minus sign between the terms (if a plus no difference)
This means that the derivatives of the terms are separate or individual
You differentiate each by itself and one at a time
There could be 15 more terms each separated by a minus or plus and you’d do each one separate.
So: f(x) = 4^x f’(x) = x*4^(x-1) Notice when differentiating you take the exponent
Multiply it times the front of the term and take one away from the exponent.
You must do this process in your sleep and fast or you’ll have trouble passing calculus
Another Example
f(x) = 15x^7
f ‘(x) = derivative
= 7*15*x^(7-1)
= 105x^6
Integration is the exact opposite
You add one to the exponent first
Then divide by that new exponent
∫[105*x^6] dx
= 6+1 = 7
So: 105*x^7 / 7
= 15x^6
Problem 1) the trig problem
Reload the attached program
First Delete the same named program from you calculator
Then reload the attached changing to “Archives” first
For the problem go to:
“trig” in my menu
Scroll to csc(x)
Find the derivative and add the 2 in the front of the answer
For arcos(x)
Scroll to cos-1 in the menu of trig
And find that derivative adding the 5 in front
“Answer the following questions about the given function: f(x)=x^3-6x^2+9
A) Find f'(x)
B) Find f”(x)
These again are separated by minus and plus signs so each is differentiated separately
f(x) = x^3 – 6*x^2 + 9
f ’(x) = 3x^2 – 12x + 0
f ‘’ (x) = 6x – 12
Notice I took the exponent and multiplied it by the front of the term
And then took one away from the exponent in each case.
Do these in your sleep!!!!!
Use log differentiation to find the derivative of the following function with respect to variable x.
(x^3+2)^3sqrt(2x^2+3)
Notice the “times” sign so you’d be thinking “product rule” or logs to differentiate
First it must be expanded:
I have expanded log problems to another base
But haven’t programmed to expand natural logs, but am in the process.
Should be done soon
(x^3+2)^3 * √(2*x^2+3
ln((x^3+2)^3) + ln(√(2*x^2+3) (always you change a square root to ^(1/2)
= ln( (x^3+2)^3 ) + ln( (2*x^2+3)^(1/2) )
= 3*ln( x^3+2 ) + (1/2)*ln( 2*x^2+3 )
Now you can choose in my menu
“log Problems”
Choose “ln(x)”
Choose “differentiate”
And add the above ln tems one at a time
Put the problem back together when finished with the individual solutions.
Calculus Q & A
Can the Calculus App do the Following?
F(x)=6x^-5
F(x)= 6x^4-4x^3+5x^2
Answer:
f(x) = 6x^5 would be “derivative/algebra” for differentiation
or “Integrals/Algebra” for Integration
I didn’t program this for myself or anyone because the student needs to be able to do these in his/her sleep. They have to learn these without programming, and they are simple
The second function is separated by minus and plus signs, so each one is a separate derivative or integral with the same minus signs or plus signs.
Derivatives you take the exponent and multiply it by the front of the problem and then subtract one from the exponent:
f(x) = 6x^5
f ‘ (x) = 5*6*x^(5-1) = 30x^4
f(x) = 6x^4 – 4x^3 + 5x^2
f ‘ (x) = 4*6*x^(4-1) – 3*4*x^(3-1) + 2*5*x^(2-1)
= 24x^3 – 12x^2 + 10x^1
= 24x^3 – 12x^2 + 10x
Now I’m not sure what you mean by “solve”?
Integrate or differentiate?
Calculus Final Solved Question 5 | Every Step Calculus
Calculus Final Solved: Question 5
Calculus Final Solved Question 2 | Every Step Calculus
Real Calculus Final Solved with TI-89 App: Question 5
Integrals on TI-89 Calculator
Use the TI-89 Calculator for Step by Step Integrals
My name is Tom and I program TI-89 calculators to make Integrals much easier step by step and showing all work.
Here’s just some of the Integral problems solved with my TI-89 Calculus App:
- Definite Integrals
- Indefinite Integrals
- Antiderivatives
- Integration by substitution
- Integration by Parts
- Partial Fractions
- Differentiation
The programs are a compilation of midterms, finals and homework from college calculus classes 1,2 and 3 all over the United States. The app shows work for calculus solutions line by line at your own pace so you can write it down on tests, homework, whatever.
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Optimization | Max Area Enclosed by Rectangle | TI-89 Calculus App
Optimization for Max Area Enclosed Rectangle on TI-89: Raw Transcript
This is a video from every step calculus dot com
demonstrating how my progams work on a t i eighty nine titanium calculator
and other calculators in the t i system for physics and calculus problems
ok this is an optimization problem in calculus and ah with regard to finding the area
given a amount of fence which is a usual problem in calculus
ah and let’s get started you put second alpha
you push second alpha to put in the i n d e x letters
and then press alpha and put in the eight and open and closed parenthesis
press enter and you’re into the menu calculus one menu
and we’re going to scroll down here to go to fence area
and we’re gonna press enter on there and a certain amount of
using a certain amount of fence how much is them maximum of area etcetera
given one side of a river and were going to put in maybe
you have to press alpha before you put any a numbers or any
characters in these lines of my programs so well press alpha
and were gonna put maybe eight fifty for the maximum fence that you have to work
with I always show you what you’ve entered
so you can change it if you want I say it’s ok
here’s a picture of it here’s the river
and you got the x on each side and the length of the other side
and generally in a problem or a test their going to ask you find the equation
for the length, here’s the equation eight fifty minus two x
write that on your paper here’s the area function
x times w and here’s the function here
write this on your paper eight fifty x minus two x squared
we multiplied x times eight fifty we take the derivative of that
here’s the derivative eight fifty minus four x
write that on your paper you gonna look like a genius
and we’re finding a critical number really critical number is not a critical point
because you haven’t found the y you’ve just found the x value
notice we took the derivative and then did the algebra computation
to find the x. write this on your paper
and here’s what you’ve found you found two thirteen on this side
two thirteen on this side and four twenty five for the length
just in case you’re interested in that they don’t generally ask you that
but they might you plug the critical number into the
original function to get the maximum area actually you’re getting the critical point
then and you do these computations and notice
that the area is ninety thousand three hundred thirteen
square units if its feet that would be square feet
if it’s meters what ever and this actually the point would be
eight fifty for the x and ninety thousand three hundred thirteen
for the y and pretty neat huh
every step calculus dot com go to my site
buy my programs and pass calculus
Integral lnx on TI-89 | Every Step Calculus Video
Integral of (x^2+1) cos(3x) | Integration by Parts Video TI89 Program
Raw Transcript
This is a video from every step calculus.com demonstrating how my programs work on a ti eighty nine titanium calculator and other calculators in the t i system for physics and calculus problems ok integration by parts with regard to finding the integral of cosine and let’s get started ahh, you have to press second alpha to enter the i n d e x letters then press alpha to enter the nine and open and closed parenthesis this is for calulus two now and three uhm and then you have to press enter and you are into my menu ahh we scroll to whatever we want right now we want integration by parts and we want cosine click on that and we’re gonna do uhm you have to press alpha before you enter anything into the entry lines of my programs press alpha I’m going to do x squared plus five times cosine of three times x. I always show you what you’ve entered so you can change it if you want. I give you that option I say it’s ok and we’re into the calulations here’s what we’re integrating. I’m not going to teach you on this so much I did on another video but we’re not interested in learning this we’re interested in doing it you can copy it on your paper or homework do it quickly there is two integration by parts on this one course it’s this formula v times u minus the integral of v times du dx. I do all this for you no problem here’s the second integration by parts because you have x times sine of three x here you can’t integrate when you have times you need to change it some how in this case doing integration by parts again and we find dv and u and du and you write all this stuff down keep writing it exactly the way it is and here’s your answer x squared plus five ect. Pretty neat huh? everystepcalculus.com go to my site. Buy my programs and pass your calculus class.
Integral of x cos(3x) | Integration by Parts Video | TI89 Calculator
Other Integration Examples on the TI-89 Calculator:
Integral of x^2*cos(3x)
Integral of (x^2+1) cos(3x)
Integral of x*cos(3x)
Raw Transcript
This is a video from everystepcalculus.com demonstrating how my programs work on a ti eighty nine titanium calculator and other calculators in the t i system for physics and calculus problems ok this is an integration by parts problem regarding cosine and uhm let’s get started here ah you press second alpha to put the letters i n d e x in here and then you press alpha to put the nine and the open and closed parenthesis you press enter and you’re into my menu index nine is a calculus two and three program index eight is a calculus one program so you scroll to whatever you want here we’re going to do integration by parts because you got cosine and doing an integral so you start here and we’re gonna do cosine we’ll press number four here and get into that we’re gonna do the integral integrate x times cosine of three x press alpha first before you enter anything into my entry lines here of my programs press alpha x times cosine of three times x. I always show you what you’ve entered so you can change it in case you’ve made a mistake. I say it’s ok press number one and we’re into the calculations you’ve integration by parts you have to find d v first this is the system and uhm etcetera. I’m not going to go to much into learning this because with my programs you just write these things down and you have the problem perfect. uhm, with my programs learning is a waste of time this is just for doing the problem and showing you exactly how to do it and uhm notice we’re taking in integration you have to take uhm the one thirds out etcetera, so that’s what’s happening here you write everything exactly as I say it and here’s your answer x times sine of three x divided by three etc. Pretty neat huh? everystepcalculus.com. Go to my site buy my programs and pass calculus.
Calculus Cheat Sheet: EveryStepCalculus.com
Use the TI-89 as the Ultimate Cheat Sheet
..
My name is Tom and I program TI-89 calculators to be the Ultimate step by step Calculus Cheat Sheet. The app show all work right on the calculator screen.
The programs are a Compilation of Midterms, Final Exams and homework from college calculus classes 1,2 and 3 all over the United States. The app shows work for calculus solutions line by line at your own pace so you can write it down on tests, homework, whatever.
You get all the calculus 1,2 & 3 programs below for the price of a serious happy hour. That all four years of calculus, updates forever included.
100% Guaranteed or your money back
LEGENDARY SUPPORT:
Phone Support (my favorite) | Email Support | Facebook Support | Twitter Support
I do it ALL and it is IMMEDIATE!
CALCULUS 1 PROGRAMS (Scroll down for 2 & 3)
Chain Rule | dy/dx = f’[g(x)] * g’(x) | dy/dx = f’(u) * u’ | (5x²+7)^5 | sin(ax) | 7*cos(5*x^2) | (tan (5x))^5 Video Example
Concavity
cos(a * x) derivative
cos(a * x) integrate
Critical Points Video Example
Definite Integral | = ∫ [ f (x) ] dx Video Example
Definition of a Derivative
Derivatives/Algebra (step by step) | √(x) | 3√(x) | 5/√(x) | 5/x | 5/8x | 5/x² | (5x)² | 5x²/8 | x(x+5) | x^½ | x^(-½) | (x²-4)/(x+2) | (x²-4)/(x-2) | (5x²+7)^5 | √(5x²+7) | (5x²+7)½ | ³√ (5x²+7) | (5x²+7)¹/³ | sin | cos | tan
Difference Quotient Video Example
ê(x) Derivatives
ê(x) Integrals
Equation of a Tangent Line (y=mx+b) Video Example
Equation of a tangent line at a pt | (y = mx + b) Video Example
Graphing by Hand | Concavity | Critical Points | Crosses x axis | Inflection Point | Intervals of Increase | Intervals of Decrease | Local Max & Min
Local Max and Min Video Example
Implicit differentiation | y³+y²-5y-x² = -4 Video Example
Integrals/ Algebra (Rewrite selected & Integrate) | n / √(x) | (x² + n)² | (x³ + n)/x² | ³√(x) | n / x² | n / ³√(x) | n / x√(x) | 1/x³
Integration by Parts | ln(x) Video Example | n*e^x Video Example | sin(x) Video Example | cos(x)
Intervals of Increase or Decrease
Limits Video Example
In(x) Natural Log
log(x) Log to Other Base | Evaluate | Solve for x | Exponential Form | Logarithmic Equation | Differentiate
Product Rule | ( f (x) )( g (x) ) Video Example
Quadratic Formula
Quotient Rule | ( f (x ) ) / ( g (x) ) Video Example
Relative Extrema
sin(a*x) Derivative
sin(a*x) Integral
Trig & Half Angle Formulas & Identities | cos(2x)2 | 1-cos(2x) / 1+cos(2x) | sin²(x) + cos²(x) = 1 | tan(x) | tan²(x) | Trig d/dx cos(2x)/2 | cos(2x) | cos(x) | cos²(x) | cot(x) | csc(x) | csc²(x) | sec(x) | sec²(x) | sin(2x) | sin(x) | sin²(x)
Trig d/dx Identities
U – Substitution
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Tom…I think that I’m finally done with Calculus II. In the prior test I got 78 and yesterday I finished all the problem on the test. I think I should be able to remain around the same grade. Thank you so much for your help; your programs really made the difference. They didn’t just solve the problems for you, in my case, they gave me the confidence and security I had lost with those stupid professors and the way they teach. To be honest, studying the programs on my calculator taught me how to solve problems that I couldn’t do before due to the way they were presented. I felt confident and secure yesterday, and it only possible because either I remember how to do the problems or the calculator would. Thanks one more time for time, dedication and quick responses. There is no other person in the whole world that would do what you do for us , college students being killed with freaking calculus classes. John
Tom- Got it to work with that link you sent me! Just wanted to say thanks for all the great work you do, and for helping me pass this calculus class. I’m going to tell everyone about this and make them pay the $30 dollars because you have done a splendid job programming my friend. Let me know if you have any new programs for derivatives or integrals and Ill let you know if I need any more help! Much thanks, –Eric
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Tommy, Great talking with you last night. I already liked you for developing this “most excellent program” but after our conversation I concluded you to be a great guy. I’ve been playing with this program most of the night, took in a few “z’s” and am back for more. This program really is superb. I did, however, notice that for some unknown reason when I attempt to do Relative Extrema’s and Trajectories that both programs came up as “Program not Found”. I’m not sure if I will be encountering the Trajectory stuff in this semester of Calculus but I do have a test this Thursday that includes Relative Extrema. Any suggestion, oh Master of this great creation?! I’m going to be gone most the day but should be home late afternoon if you got time to call. Same number (843-xxx-xxxx). That’s Myrtle Beach, 3 hours ahead of you and more golf courses than you can shake a stick at. Thanks -Joe
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Gradient | Definition | 2 Variables | 3 Variables
Implicit Differentiation Video Example
Trig & Half Angle Formulas | 1 + cos(2x)2 | 1 – cos(2x)/1 + cos(2x) | 1 – cos(2x)/2 | cos(2x) | cos(x) | cos²(x) | cot(x) | csc(x) | csc²(x) | sec(x) | sec²(x) | sin(2x) | sin(x) | sin²(x) | sin²(x) + cos²(x) = 1 | tan(x) | tan²(x)
Linear Equations (3 variable) | ax+by+cz+d=0
Line Integral Over Range | = ∫ ( f [(x(t),y(t),z(t)] * √ [ x'(t)² + y'(t)² + z'(t)² ] ) dt
Mass of Spring or Wire
Magnitude of a Vector | r(t) function
Parametric Equation | r(t) function
Partial Fractions Integration
Polar to Rectangular Conversions
Projection of Vector A on Vector B
P & Q Vector Points | Position Vectors | Projection of a on b, b on a | Speed
Quadratic Formula
Sketch a Graph | r(t) function | Make a Table of Points
Surface Integral | x,y | x,z | y,z
Position Vectors | Velocity | Acceleration | Speed | Unit Tangent Vector | Parametric Equation | Standard (Linear) Equation
Speed | r(t) function
Sphere | Center Point | Mid Point | Equation | Radius
Surface Area Revolving
Surface Integral | x,y | x,z | y,z
Tangent Plane to a Surface
Trig d/dx – Identities and Functions | Half Angle Formulas | Reciprocals | Integration | Derivatives | 1+cos(2x)2 | 1-cos(2x) / 1+cos(2x) | 1-cos(2x)/2 | cos(2x) | cos(x) | cos²(x) | cot(x) | csc(x) | csc²(x) | sec(x) | sec²(x) | sin(2x) | sin(x) | sin²(x) | sin²(x) + cos²(x) = 1 | tan(x) | tan²(x) Video Example
U Substitution
Vectors | Unit Tangent Vector | Unit Vector PQ/||PQ|| | Vector Between P & Q
Velocity
Volume of a Parallelepiped
Work | Force Field | Lifting Object | Spring | Pumping Oil
Don’t forget the programs come with my
LEGENDARY SUPPORT:
Phone Support (my favorite) | Email Support | Facebook Support | Twitter Support
I do it all and it is immediate.
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Calculus Cheat Sheet Video Transcript
Ok, today I’m doing a calculus cheat sheet video, many of you have asked about that,
and I’m going to do one for you here on my programs. There is no better cheat sheet
for calculus than my programs in your Titanium calculator, you load them in there. All you
want from a cheat sheet is a formula, and how to do the problem, step by step, to solve
the problem, so that you can either memorize it or learn it or help you. You’re not interested
in learning it, not interested in memorizing it, I understand. Even better in my programs,
you can add your own variables in my programs, where you can’t on a cheat sheet, so therefore
you get the actual calculations and the actual answer. A cheat sheet gives you formulas and
that’s the first thing that my programs do. When you run my programs, I give you the
formula and you write that down on your paper, the first thing to get started. And then you
go from there. So let me show you about my menu a little bit here. To get to my menu
you have to press index, put in this formula here, index eight closed parenthesis, you
do that by pressing second alpha on your calculator, and putting in these letters, I n d e x, and
then pressing alpha again and put in the eight and the closed parenthesis, and then you press
enter and then you’re into my programs. You have vectors, notice a and b vectors,
and you have x,y, and z vectors but if you only have two vectors you can put zero in
for the z variable. And you scroll down look at acceleration, arc length, chain rule, concavity,
I do graphing by hand in my programs, critical points, there’s more graphing by hand, cross
product is a vector calculation, curl for calculus three, definite integral, definition
of a derivative which is really difference quotient here. That’s the first week of
calculus very very difficult and very, very useless, dot product, all kinds of things
here, e to the x integrating, exponential functions, and uhm, implicit differentiation
that’s always good. Ah also all the way down for many, many different things, even
has something for money in here if you want to find the time value of money equations
for calculus, of course we have the quadratic equation, where you can just get the answer
by putting in your variables in your equation or I do it step by step, if you want that,
quotient rule, speed, calculations for a sphere, mid point, sphere equations, volumes for a
sphere, radius, and of course trig and half angle formulas, which are very important because
the calculators cannot enter secant or cosecant and you need to convert those to sign or cosign
to be able to do that and of course I give you the integrals and derivatives of those
trig functions, there’s no step by step its just memorization. So check out my web
site. www.EveryStepCalculus.com and now also www.EveryStepPhysics.com
don’t forget my physics programs, ah and have a good one.
What Professors don't tell you about ln(x)
Any problem with ln(x) in it you’d choose ln(x) in my program menu
When differentiating ln(x) and when using the product rule which is necessary, where the function might be something like 5*ln(6x). You have two functions –—— 5 and ln(6*x). Two functions mean f(x) and g(x).
In my programs I used in this case 5 for f(x) and ln(6*x) for g(x)
And you have the formula for product rule, h ‘ (x) = f ‘(x) * g(x) + f(x) * g ‘ (x)
Don’t worry – I do all of this for you – step by step – in my programs, however I want to mention here of again what professors don’t tell you or make you aware of, and that is
If ln(x) has a + sign or – sign in it, it makes a difference which one you use for f(x) or g(x) so for instance in a function like 5*ln(6x+1), you have to use instead of 5 for f(x) (like above) — ln(6x+1) for f(x)
Now who told you or me about that little detail in our calculus life?
Incidentally any derivative for ln(x) has a special formula which is:
u ‘ / u
u is what’s inside of the parenthesis.
Have fun with my programs and pass calculus, never to use it again !!!
Tom
Calculus Solver Software | Solve Calculus Problems | App
Raw Transcript
Ok this is a video on a calculus solver for calculus problems, my programs are
perfect for solving all kinds of solving calculus questions and problems. The are
designed for tests really, I’m not interested that you learn it or that you memorize
it, I am interested that you learn enough to pass tests and get out of calculus
somehow. That’s what my programs were designed for me to do, and hopefully
for you if you purchase them. Anyways let’s get started – you press second
alpha to put the I n d e x in the calculator, then you push alpha eight and closed
parenthesis to get to my menu, then you press enter and up comes my menu.
You can scroll down for many, many different things. I have graphing by hand, ya
know, concavity and vectors where you can put in a and b vectors. Here’s cos of
a and b which is two vectors, and you find the angle of it. Definite integral,
Definition of derivative, which is pretty interesting. Equations of lines, integrate,
gradient, graphing by hand, implicit differentiation, Inflection point, graphing by
hand, limits, line integral, log – p and q points – P and Q points is interesting
because that’s in calculus three really, because they give you the end points and
these vectors show direction, where the other vectors show just, they are really
called scalars, but this is actually a directional vector, when you get p and q
points, x y and z variables. Well let’s do p and q points here to see what
happens. Wait for it to load here, and you’re going to put the – you’ll notice your
going to have to put the x value in, you’re going to have to press alpha and put
eight, that’s what they’ll give you in test, and then you are doing the y value, and
so your going to put alpha minus nine, and then alpha, I don’t know maybe put
four in here. An then we’re going to do the q point of the vector, again alpha,
let’s go minus five, alpha minus eight, and alpha ten. I show you the points, what
you’ve entered, see if you want them right, you look at your test to see if you’ve
entered them correct, and then if they’re correct, we press ok, and we can do all
kinds of these different things, sphere equation, we can do sphere radius, we
can scroll down to sphere radius – sphere remember is calculus three because
we’re into spheres, which are three dimensional things. Here we have the mid
point, we can go mid point here. Center of a sphere is a mid point and it’s given
by pq, I give you the formulas, and here we have four minus eighteen over two,
and then calculates to that vector. Standard equation, press five, these are all
standard equations – center point, press two, center of a sphere is the midpoint
and is given by pq, there’s the center again, we already did that. Radius, there’s
radius, it’s a square root and then squares within the square root, approximately
seven point eighteen units. So make sure that when you look for a calculus
solver, that you are looking at my programs, because on the Titanium there is no
better solver for calculus than what my programs do, people have said that over
and over again. Every step calculus dot com, check it out.
Integrals
Raw Transcript
This video is going to be on integrals, rewriting an integral, and also evaluating one. Lets get started – you have to press second alpha to put the letters of this code in – you just do this once and up comes the menu for you – and you push alpha and then eight and closed parenthesis, and then press enter, and up comes my menu of all the items – I know that what I want to go to is the letter p, they go from numbers here, but then they go p, so you can scroll down like this, all the way down – or if you know what your after you can go alpha and then p, and I’ll go to – I want to rewrite the integrand first – so I’m gonna – one of the most important parts – I tell you one of the most important parts in here – and so
you kinda go to this list here – and these are the tough ones – so you go to your list and like for instance let’s do number six here – press number six – n over x squared – you need to convert the denominator always to a numerator, and that in algebra becomes x to the minus two, n times x to the minus two, and then you integrate – you’re going to go integration of n to the x to the minus two – which you can do it now, and here you have – n to – notice you add one to the exponent up here and then all this you divide by that also – minus two plus one – that equals n to the minus 1 – minus one. So that equals minus n over x – and you can go to another one here, lets try number 5, here’s the cube root – well cube root of course is exponent of, to the one third, and to integrate x to the one third, you have to add one, well one in one third is three thirds, so you add that and divide, and put that in the denominator also, and you have x to the four thirds over four thirds, and when you divide by a fraction you invert and multiply, and so here’s the answer, three x to the four thirds, over four. Ahh pretty neat huh, well I wanna do, I’m going to go here and quit, lets scroll down here – and we can quit on either end of it – press enter – now if you wanna, I’m gonna go alpha and p again to get back to the program, I’m gonna – I want to evaluate, I’m gonna press number two, and evaluate – and for demonstration let’s just do uhm – you have to press alpha before you enter anything in this line here – alpha, and let’s go uhm – t times uhm – sometimes they use the variable t – times – let’s use e to the x here, e to the x of three times, t squared. And it shows you what you’ve entered here – I show you – and you can go ok or change it – I’m going to say it’s ok, so – and I don’t do it step by step particularly – uh – because this is u substitution – uhm – but anyways – ah – this is the exact answer. And so that will help you immensely – ya know – checking your integrals with any type of integral – quickly – and the step by step I have in other sections of my programs like for instance u substitution – so – fabulous programs, check em out at everystepcalculus dot com
Difference Quotient, Calculus App, TI-89 Titanium
Difference Quotient, Calculus App, TI-89 Titanium
Raw Transcript
Hello, this is Tom from everystepcalculus.com. I’m gonna do the difference quotient for you today or what others call the definition of a derivative.
We’re gonna get started. Turn calculator on, press 2nd Alpha and put index the alpha again, then 8, then () and press enter. Up comes my program menu, you can see the things I’ve programmed so far. There is a graphing section with the calculus and graphing, maximum and mins among others. But today we’ll be doing a definition of a derivative or difference quotient, which ever you know, either one will take you to the program. Press enter and you are in the actual program. Every time you see pause here, you can enter. We’re gonna put in an example, for instance, (you have to press alpha first when you put anything for these boxes) I like to use 7*^2-7*x. Now you’re gonna substitute for every x in the function, x+h
Should look like this: f(x) =7*x^2-7*x select ok or change it if you want. This is the formula, the f ‘ of x = the limit as h goes to 0 h represents the change of x.
Formula should be: f’ (x) = lim
h->0
= f (x+h)- f (x)
h
h represents x
Jot down on your paper then put in your function. Notice I’ve substituted “x+h” for every function and the original function all divided by h.
F’ (x)
7*”x+h”^2-7*”x+h”
= -(7*x^2-7*x)
h
Very complicated program, took me a long time, maybe a month to do this program. Worked a lot with research to do it, calculus books and such. So, you’re gonna write this on your paper, but you’ve taken the x squared of the function and worked it out.
F’ (x)
7*x^2+14*h*x+7h^2
“-“ (7*(x+h))
-(7*x^2-7*x)
h
Keep writing these down and eventually you’ll get:
F’ (x) = lim
h->0
=14*x+7*h-7
@ h=0
Answer
= 14*x-7
And you’ve gotten a hundred percent on that problem and you look like you know what you’re doing and everything else.
Everystepcalculus.com you can go to a new problem, main menu or you can quit or do what you want.
Enjoy my programs