Transcript

Hello, Tom from everystepcalculus.com and everystepphysics.com again. This is a problem that was sent in by a student to Yahoo integrate X times the quantity X squared + 4 to the ½ power. So, let me show you how we do that in my programs okay. Index 8 to get to my menu we’re gonna go on a scroll up to get to U substitution the reason you know it’s U substitution because you take the derivative of what’s inside the parentheses here. Which is 2x and that is almost matching the outside of the problem except for the two you know and so then that’s someone my say that might be U substitution. So, then you go to use substitution in my programs, here we go there and we’re gonna enter the function you have to press alpha first. Alpha X times the quantity X2 plus four close off the parenthesis to the left parentheses, 1 divide by 2 power and you noticed the calculator and I would do anybody in a mathematician would you changed anything to the half power to a square root situation. Until you get into integrating it then you change it back okay so, this is the problem here I wish to give you a chance to change in case you made a mistake but that’s the correct one and we’re waiting for the program to load. So, here’s the problem we’re gonna rewrite it with the X next to the DX okay I like to do that because it keeps you organized as far as what you’re doing with the next step which is the most important one. Remember this one forever this is the one very simple U equals at the inside of the parenthesis okay, the derivative of that is 2X is DX. We take the 2 with algebra and divide it than the other side by ignore size by two with XDX notice this is the same is what we rewrote the problem with okay. So, you can forget about that portion of it now, we have integral of this right here so that’s the same thing as the integral of the square root of U, DU divided by two okay constants come out of the integral course and you do this write this stuff down exactly as what you’re looking at here. Excuse me that is a firetruck coming by and here’s the answer right here. Okay, pretty neat huh everystepcalculus.com go to my site buy my programs are only $40.00 nothing like you’d spend in a bar or a pizza house or out to dinner and yet you have this stuff in your calculator forever able to do all these problems, hundreds of problems in my; in the calculator okay. This is the greatest notebook because when I research a problem why? Why would I just put it on a piece of paper and throw it out you know I program it put it in here I have it for the rest of my life and you will too if you buy my program so keep that in mind and you’ll be able to pass calculus because you’ll get six or seven problems exactly right in any test of calculus compared to the guys or girls sitting next to you and of course the class is scored on partial credit and the class curve. So, that’s the reason that you don’t need to get a hundred percent on every test to get an A or pass the class or test. Hey, have a good one.

## Long Division, (x^5+x^2)/(x^2-1)

Transcript

Hello everybody, this is Tom from everystepcalculus.com and everystepphysics.com. Doing a long division of functions problems with my programs showing you how that works, index 8 to get to my menu we are already at long division you will scroll down to that when you want to do it or whatever problem you want to tackle with my programs and we are going to enter the function and you have to press alpha before you enter anything in these entry lines here, alpha (x^5+x^2)÷(x^2-1) you notice now that your it up just like a regular division long division problem and numeric numbers her is your dividends (x^4-x^3+^2) and this is the divisor (x-1) there is no name particularly for the this line here and this line is not hieratical it’s a divisor line, so we are going to set it up like this and we are going to divide x into x 4 first and then whatever answer which is called the quotient your going to multiple that times both of these times here I’ll show you that in the next, busy means it’s loading the problem and it only happens slow like that when the first time you load it otherwise it’s very fast so x and the x4 is x^3 okay and x ^3 times x is x ^4 and you are going to subtract that right down here and this is equal to zero and then you are going to have x ^3*-1 which is a minus x^3 and you change the sign because you are subtracting so that’s a positive x ^3 and these will also cancel so what is left is x^2 here and you pull that down and all the rest have cancelled and since x ^3 can’t go into x ^2 you are all done with the problem and therefore this is pulled down here and then they’re divide by the divisor and your answer is (x^3)+(0)+(x^2)/(x-1). Pretty neat huh everystepcalculus.com go on my site buy my programs and enjoy passing calculus, have a good one.

## How to solve: ∫(√(x))dx / √(1-x)

Let √(x) = sin(u)

Differentiate both sides

= 1/(2*√(x))dx = cos(u)du

So:

dx = cos(u)du / 1/(2*√(x))

= cos(u)du / 1/[2*sin(u)]

Invert and multiply

= cos(u)du*2*sin(u)

So:

∫√(x)dx / √(1-x)

Substitute

= ∫sin(u ) * cos(u) * 2*sin(u) / √(1-sin(u)^2) du

= ∫ 2*sin(u)^2 * cos(u) / √(1-sin(u)^2) du

Identity

= ∫ 2*sin(u)^2 * cos(u) / √(cos(u)^2) du

= ∫2*sin(u)^2 * cos(u) / cos(u)du

cos(u) cancels

= ∫2 * sin(u)^2 du

Identity

= ∫2*[1 – cos(2u)]/2du

= ∫ [1 – cos(2u)]du

= ∫(1)du – ∫cos(2u)du

= u – (1/2) * sin(2u) + C

Identity

u – (1/2)(2) * sin(u) * cos(u) + C

u – sin(u) * cos(u) + C

Back substitute

**Answer:**

= sin-¹(√(x)) – √(x) * √(1-x)”

## Time Value of Money

### Time Value of Money using Calculus

### $1000 present value

### 7% yearly interest rate over 6 years

### What is the Value (future value)?

Raw Transcript

## Line Integral

Raw Transcript

Hello again; Tom from everystepcalculus.com, everystepphysics.com. I’m going to do a line integral in calculus 3 physics. This is right off of Paul’s notes, his example. You can check if you Google line integral. None of us are interested in line integrals; all we want to do is know how to do the problem to pass a quiz or a midterm. Very difficult. I’ve tried to find what does a line integral represent. In other words, what’s the SI units for the answer that they get, and I can’t find it. So that shows you something about calculus. To me, most of it is nonsense. Index 8 to get to my menu. I’m going to scroll down to line integral. I’m already there to save time. And we’re not in a vector field we’re given the RT situation. And I show you the formula; this here is the formula: RT times the magnitude of R of the derivative of RT. And then this worked out. This is RT here, and then the magnitude absolute value of R, derivative of RT is this. Write this all down in your paper, exactly as you see it so you look like you know what you’re doing. And we’re going to put the RT was given in this a problem. We’re going to do alpha before you enter anything into these entry lines here, alpha 4 times 2nd cosign of T alpha 4 times 2nd sign of T. And when they don’t give you the Z, you just put 0 in. Alpha 0. Now it will show you what you’ve entered; you can change it if you want. I say it’s okay. Now we start working out the‚this is a vector here when you have these arrows on these sides, it’s called a vector, RT vector. We’re doing the derivative of that, which equals minus 4 sign of T and 4 cosign of T, et cetera. And we do the magnitude, which is squaring those derivatives. And the answer turns out to be the square root of 16, which is 4, really. And then we’re going to enter the function given, which is alpha X times Y to the fourth power. Where they dream up all these nonsense formulas and functions is unbelievable in calculus. I say it’s okay; you could have changed that if you want. So for the range of alpha, minus pi divided by 2 to the range of alpha pi positive divided by 2. So here we have the range, and here we have the function, and here we have the derivative magnitude of the derivative of RT function. And you do the calculation just as you see them here on your paper. Over the range of this here, you’ve already done the derivative here. Here’s the derivative of that. The answer is 8192 over 5. Notice now it’s just an arbitrary number. We’d like to know area or something, distance, or length or something, but it’s just a number. So you have to decide yourself how important that is. I mean, to me, how important is the slope of a line, which is the derivative or the area under curves, or volume under functions, under spheres and stuff. Have a good one. Go to my site, subscribe and you can see more movies that I might make.

## Difference Quotient Solver

## Difference Quotient Solver

## Step by Step Calculus Solver

## Step by Step Calculus Solver

Raw Transcripts

Hello, Tom from everystepcalculus.com, everystepphysics.com. Don’t forget physics, either, in your schooling. I‚m going to do two problems in calculus: a definite integral, and a log problem. I’ll show you the diversity of my programs. And my programs turn the titanium into a calculus calculator with steps. A calculus calculator with steps‚ that’s exactly what my programs do. So let’s do it. Index 8 to get to my main menu. We’re going to scroll down to definite integral in the D’s. Definite integral in X because you only see X in the problem, right? We’re going to enter the function. You have to press alpha before you enter anything into these entry lines. You’re going to press alpha, and we‚re going to enter the function. 3 minus X to the cubed plus 4 times X. Now we show you what you’ve entered; you can change it if you want. I say it’s okay. I’m going to enter the range. Lower range is alpha minus 2. Upper range is alpha 2. I say that’s okay also. And we integrate it, which is this right here. We’ve integrated each one of those terms, separated by plus or minus signs. And at the upper range, X equals 2. You add these into the‚ you’re going to use, instead of quotation marks, you’re going to use parentheses around your additions into the main function. But it equals 10. And if X equals minus 2, the answer is minus 2. Upper minus lower is equal to 12 square units. Pretty neat, huh? All right, we’re going to go back to the main menu. Number two: And we’re going to scroll down. Now this is in the L section, logs. So I’m going to do this quick. Behind the simulator here I can only use, I only have one essential finger to do this with. On your calculator, the titanium, you can hold the 2nd down with your thumb or finger and press this. It’ll go screen by screen and really go quick down to logs. We have natural logs and all kinds diversity in my menus. I’ve done all the calculus problems, or most of the tests, of course. Nobody can do all of the calculus problems; there’s millions of derivations of that. Log problems, okay. We’re going to evaluate this log problem, number 3. We have to press 2nd alpha to get to the letter register to put log in. We’re going to enter the problem. We want to make, we have 2nd down here, but we want to turn it to black like that. Then we can put the logs in there, so that’s‚Äî The letters appear over the numbers, you can see them. And then we’re going to go back to numbers, which erases that black mark there, indication. And we’re going to put 3 parentheses 1 divided by 27. Close off the parenthesis. And I show you what you’ve entered. It looks pretty good to me. We’re going to press 1, and here’s the answer step-by-step. In other words, if you on your calculator, if you put 3 to the exponent minus 3, you’re going to come up with 127. All right. Pretty neat, huh? Everystepcalculus.com. Go to my site. Buy my program if you want to pass calculus or physics. Or subscribe so you can see more videos. Have a good one.

## Implicit Differentiation Calculator With Steps

## Implicit Differentiation Calculator With Steps

Raw Transcript

Hello everyone; Tom from everystepcalculus.com and everystepphysics.com. Don’t forget physics. I have turned through the use of my programs, or for programming, your titanium calculator into an implicit differentiation calculator with steps. And that’s exactly what my programs do. So let’s do it. Index 8 to get to my menu. I’m already at implicit differentiation. I’ve scrolled there. On your titanium, if you want to go to my menu and go down quickly, you hold the 2nd button down here and then use the down cursor here. We’re already at that, so. And then enter the function. You have to press alpha before you enter anything in these entry lines here. And the problem is alpha Y squared plus 3 times X minus 8 times Y plus 3 equals 0. Now it will show you what you’ve entered, and you change it if you want. I say it’s okay. You’re differentiating all of the terms on both sides of the equals sign. You must have a 0 or a constant on the right of the equals sign. You have to use the algebra to make that happen if they give you a more difficult problem, or a different look at a problem. And so we differentiate each one of the terms. I do that for you; you write this on your paper as we go through it, exactly as you see it here. And we combine the DY DX terms, separate it from the other terms, and here’s the answer right here. Now we want to evaluate it at a point, so we’re going to press the X value is alpha 4 and alpha 3. I show you that also; it looks good to me. So we’re substituting 4 and 3 for the X and the Y values and then find the derivative. Cut them to one half and the slope of the line is 333 degrees. That means that the slope is going to be here’s 360 going this way. Here’s 270 going down. So the slope is going to be like this. Pretty neat, huh? Everystepcalculus.com. Go to my site. Buy my programs if you want help passing calculus. Or subscribe to enjoy more videos that I might make. Have a good one.

## Calculus Calculator with Steps

## Calculus Calculator with Steps

Raw Transcripts

Hello, Tom from everystepcalculus.com, everystepphysics.com. Don’t forget physics, either, in your schooling. I’m going to do two problems in calculus: a definite integral, and a log problem. I’ll show you the diversity of my programs. And my programs turn the titanium into a calculus calculator with steps. A calculus calculator with steps, that’s exactly what my programs do. So let’s do it. Index 8 to get to my main menu. We’re going to scroll down to definite integral in the D’s. Definite integral in X because you only see X in the problem, right? We’re going to enter the function. You have to press alpha before you enter anything into these entry lines. You’re going to press alpha, and we’re going to enter the function. 3 minus X to the cubed plus 4 times X. Now we show you what you’ve entered; you can change it if you want. I say it’s okay. I’m going to enter the range. Lower range is alpha minus 2. Upper range is alpha 2.

I say that’s okay also. And we integrate it, which is this right here. We’ve integrated each one of those terms, separated by plus or minus signs. And at the upper range, X equals 2. You add these into the you’re going to use, instead of quotation marks, you’re going to use parentheses around your additions into the main function. But it equals 10. And if X equals minus 2, the answer is minus 2. Upper minus lower is equal to 12 square

units. Pretty neat, huh? All right, we’re going to go back to the main menu. Number two: And we’re going to scroll down. Now this is in the L section, logs. So I’m going to do this quick. Behind the simulator here I can only use, I only have one essential finger to do this with. On your calculator, the titanium, you can hold the 2nd down with your thumb or finger and press this. It’ll go screen by screen and really go quick down

to logs. We have natural logs and all kinds diversity in my menus. I’ve done all the calculus problems, or most of the tests, of course. Nobody can do all of the calculus problems; there’s millions of derivations of that. Log problems, okay. We’re going to evaluate this log problem, number 3. We have to press 2nd alpha to get to the letter register to put log in. We’re going to enter the problem. We want to make, we have 2nd down here, but

we want to turn it to black like that. Then we can put the logs in there, so that’s—The letters appear over the numbers, you can see them. And then we’re going to go back to numbers, which erases that black mark there, indication. And we’re going to put 3 parentheses 1 divided by 27. Close off the parenthesis. And I show you what you’ve entered. It looks pretty good to me. We’re going to press 1, and here’s the answer step-by-step. In other words, if you on your calculator, if you put 3 to the exponent minus 3, you’re going to come up with 127. All right. Pretty neat, huh? Everystepcalculus.com. Go to my site. Buy my program if you want to pass calculus or physics. Or subscribe so you can see more videos. Have a good one.

## Green’s Theorem

Raw Transcript

## TI 89 Partial Fractions

## TI 89 Partial Fractions

## U Substitution Calculator

Raw Transcript

## Critical Points-Work Shown on TI-89-Video

Transcripts

Hello, Tom from everystepcalculus.com,and everystepphysics.com. A problem in calculus dealing with critical numbers in critical points of a function. Let’s do it. Index 8 to get to my menu. Then your going to scroll down to critical point or numbers.I always have you start a graph on your paper. When you enter the function you have to press Alpha before you enter anything into these entry lines. Your going to press Alpha X cubed minus 3 times X. I always show you what you’ve entered. You can change it if you want. I say it’s okay. And we’re gonna choose number five, critical points.

## Triple Integral: Work Shown on TI89-Video

Transcripts

Hello again, everyone. This is Tom from everystepcalculus.com and everystepphysics.com. I’m going to do a Triple Integral for Calculus 3 right now. This is an example of a Patrick JMT, my favorite instructor on the internet, on YouTube. So I’m going to show you how it works on my program. I don’t know anybody can do that problem. He can do it because he’s a genius. But for us students,etc. How do we do it? Let’s get started. Index 8 to get to my menu. I’m going to scroll up because I can go to the bottom of the menu then instead of going down quicker to go to the T’s section. And we’re going to choose Triple Integral. And we’re going to enter our function. You have to press Alpha before you enter anything into these entry lines here in programs, okay. Alpha x times sin of Y. I always show you what you’ve entered. You can change it if you want. And we’re going to use the order of integration which is dx, dz, dy which is in the example. You have the other choices in case that’s given on test also. And we’re going to enter region q. Enter these limits. This is Alpha 0 for the x one Alpha square root of 4 minus z squared I made a mistake so I gotta go back. Choose number 2. Alpha 0, Alpha square root of 4 minus z squared. Close up the parentheses. That’s better. I say it’s okay. Next one for the y is Alpha 0. Alpha pi. That looks okay. and Alpha 0 for z. Alpha 2. That’s okay. So here’s what you write on your paper. The way you write it with triple integral with dx dz dy order of integration. Here’s the function in here. So you’re going to do the dx first and you put this over here with these lines. Showing you’r doing a range over this integration here. And here’s the integral of the first function okay. And if x equals the upper range. I show quotation marks here but you put you put parentheses in there. Because you’re substituting this amount for an X in the integral. And it equals this, minus sin, etc. And then we do the lower integral. X equals 0 and there’s 0 and you put parentheses around this instead of quotation marks, okay? And here’s the answer, you have the upper range minus the lower range equals this right here. So that becomes the new integration function. And I show you that here. dz dy is left, okay. So now we integrate that. Come up with this. Minus sin, etc. over this range here 0 2. Add z equals 2 Here’s the answer here. And z equals 0. Plug these in for all the Z’s in the problem. And the answer is this. 8, the upper range minus the lower range is 8 sin y divided by 3. Now we’re going to use that for the integration function. With the range of 0 and pi. At y equals pi minus 8 cosine is 8 thirds.