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Partial Derivatives First Order

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Hello again, everyone, this is Tom from everystepcalculus.com and everystepphysics.com. I’m gonna do partial derivatives now in this video, generally with respect to calculus 2 or 3. Let’s do it. Index 8, get to my menu… Scroll up to get to the P’s quicker. It goes to the bottom of the alphabet, so we get to what we’re looking for, it’s partial derivatives. On the menu you can go second and the titanium second and then these cursers to go page by page. You do that here to get through the menu quicker, and we’re looking at, let’s see, partial fractions, here’s partial derivatives, and I programmed first order or second order; we’re going to do first order in this problem. Z= f (x,y) We’re going to enter our function, that the function given is. You have to press alpha before you enter anything into these entry lines in my programs, okay, so alpha, and then we’re going to press T here, which gives us the arc tangent for Y divided by X I always show you what you’ve entered so you can change it if you made a mistake. So it’s okay, and here’s the partial derivatives, with respect to x, is minus Y divided by X squared plus Y squared, this is a, if you go to my trig identities you’ll see that tangent to the minus 1 is 1 over the quantity of 1 plus x squared. In this case it would be 1 over the quantity 1 plus Y divided by X squared. To get the derivative with respect to X and with respect to Y, it’s this equation here. And then there’s a point A and B that they give you. Press the one for A, is alpha, minus 2. Make sure you know it’s interchanged the minus sign for the negative sign. And then for the B, alpha 7 is given. Again I’ll show you what you’ve entered, and we see that’s okay, and so the problem asks for fx(a,b), which is this right here, replacing the y’s and the x’s for whatever is given here for A and B. And I have to use quotation marks the way the calculator allows me to with programming, but you’re going to use parentheses here anytime you see a quotation here, because you’re substituting X and Y values for the X and Y values in the function. And the answer is -7 over 53. And now if they ask you for F of Y you’d go one step further, and that would be substituting this, you get -2 over 53. Pretty neat, huh? everystepcalculus.com, go to my site and subscribe to me so you can see other videos if you’re interested. Have a good one!

Calculating Integral with Shell Method

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Hello, everystepcalculus.com. We’re gonna do a problem in Yahoo regarding Shell Method and show you how that’s done in my programs. Index 8 to get to my menu. Then I scroll… if you go up, you get to the bottom of the alphabet because S is closer to W than A. And then we’re gonna find shell method, which is there. This problem is vertical axes number 2. Shows you this formula. They ask you if p(x) is the radius and is this second value given for X, and yes it is. We’re gonna add that alpha. 4 times X squared and the next value for Y is given. Alpha 24 times x minus 8, times X squared. I always show you what you did, and that was not correct so I have to go back and change it. Alpha 4 times x squared… I don’t know why it wasn’t right. Alpha 24 times X minus 8 times X squared. That’s better. Say it’s okay. Are the limits given, no, they’re not given. So we have to compute the limits, so we choose number 2. We do that by setting the… if no amount is given for the x axis of revolution then the vertical axis is 0; x=0. Anyways, we set the two functions equal to each other and then solve for x, when x equals 0 or 2. That’s where these functions intersect the X values where the Intersect. And so the height then needs to be recalculated. Height is the original function less than p(x) which equals this here. And then we’re ready to do our here’s the limit, 0 and 2, we do the calculation. Here’s the volume for the solid, the formula, notice x is for the radius and this is for the heights. And we multiply them together, we get this here. And we do the integration, which is this this: 8x cubed minus 3x to the fourth. And then at x=2, I’ll show you, these quotation marks here are you’d put parenthesis in there because you’re substituting 2 for all the x values. That equals 32 pi. And x=0, you substitute that in there, becomes 0 of course, so the answer is 32 pi. Have a good one.

Related Rates – Pulley Rope

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A boat is being a pulled into a dock by a rope attached to it and passing through a pulley on the dock positioned 8 feet higher than the boat.  If the rope is being pulled in at a rate of 2 meters per second, how fast is the boat approaching the dock when it is 9 meters from the dock?

Raw Transcript

Hello, everystepcalculus.com, a problem in calculus with related rates: a boat being pulled up to a dock, where the dock is higher than the boat problem. Let’s do it, you can see the problem on your screen. Index 8 to get to the menu, we gotta go up to… gonna go up on the cursor so we can go to the bottom of the alphabet to get to the R’s quicker. This is calculus 1 but also it’s in calculus one, two, and three. Related rates and we’re choosing the “Boat/Dock pull”, number 2, and we’re gonna enter our parameters. We have to press alpha before we enter anything into these entry lines here. Alpha, the height is given as alpha 8 meters, the ropes rate of change is equal to alpha 2 meters per second, it’s decreasing because it’s going closer to the Y axes. It’s pulled in, enter distance from the dock is alpha 9 meters. I always show you what you’ve entered, you can change it if you want. I say it’s okay, and I give you the perimeters, now what we’re talking about here, x equals distance from the boat from the dock and y equals the height of the dock above the boat, and L equals the length of the rope, which is the hypotenuse. And of course dL/dt is the rate of change of minus two meters per second. Given. So we find the length of the rope, which is equal to the square root of 145. Pythagorean theorem. And then we formulate the same equation basically but we work out a little bit different because we’re gonna do the derivatives of everything here. So um we do the derivatives you read all this on your paper, you do all the derivatives of the whole function before, just like this, and that’s the answer. Really the answer is square root of 145 times a minus 2 divided by 9, which is dx/dt which is the change of rate of the x axis as the boat is being pulled up the dock. And the approximate answer is -2.6759 meters per second. Have a good one.

Time Value of Money

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Time Value of Money using Calculus

$1000 present value

7% yearly interest rate over 6 years

What is the Value (future value)?

Raw Transcript

Hello everyone, Tom from everystepcalculus.com, everystepphysics.com Problem with regard to money which I know is on a calculus test, but it’s gonna be in my menu so I can give you an example of how my programs work. So let’s do it. Index 8 to get to my menu. And we’re gonna press 2nd, and the cursor control down to… this goes page by page, so it’s a little quicker. Go down to “money”. And we’re gonna choose “money over time” and compute it over a yearly amount of time. That was the formula before. We’re going to enter the present value of the money we’re talking about. Alpha 1 thousand dollars. Interest rate, alpha 7 percent; make it a decimal, we divide by 100. And number of years, let’s choose number 6. I always show you what you’ve entered, you can change it if you want. Say it’s okay. And the value is gonna be 1521 dollars and 96 cents six years from now, based on 7 percent interest. Go to my site, well, you are on my site if you choose this menu, but subscribe so you can see other videos that I might make. Alright, have a good one. One more thing, we’re gonna go back here and just tell you one more thing. Money over time, we can also choose, you know, the number of periods, for instance, a yearly period will be 12 periods and and then semi-annual would be 2, and quarterly would be 4, so remember that if you do– and then also, you can send me a money problem if it’s not in here, I’d be glad to incorporate it in here, I like to make everything as complete as I can, so don’t be afraid to do that either, and I’ll try and program it for you. Alright, have a good one.

 

Simpsons Rule on TI89

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For more info and videos visit our Simpsons Rule master resource page.

Raw Transcript

hello Tom from every step calculus dot com every step physics dot com problem in calculus I involving the simpson approximation system I’ll finding the area under a curve you and I’m let’s do it index eighty it to my menu I’m a scroll up to go to the s section which is simpson alphabetical Simpson’s rule there is there and we’re actually doing the integral you know a definite integral here a to be and simple way of doing it and then simpson or makes it hard n some more nonsense and now home a lotta calculations do the same thing his calculus is famous for arm surrender a function function is if the press of the freeman or anything in the central issue in my programs also for minus X square I’ll show you what you know you can change it if you want and the range given is alpha for and alpha 6 now looks pretty good we can say that’s okay in the intervals given they wanted from 6 a.m. alpha six and here’s the formula for Simpson’s rule here make the same your paper s exactly what it is you look like a genius and the change in taxes Delta X course B-minus a divided by and which is one-third and at an equal six we’re gonna do find out the X values x0 in the collection not original X is a a the 4s the lower it interval and then x1 you write notes Fort 1303 Asus computer says a less the changeover dealt actual to just computer times one at times to et cetera and we do that for the six inch wheels me play certain function turns out to be true placing me effort for into the function here -12 minus 133 over nine -1 sixty over nine -21 -2 2009 -2 53 overnight and -32 and so we’re gonna uses simpson proxy nation to to do this in a row here and that someone is this right here after me and then four times exit 12 times except you four times exit 32 times except for four times exit 5 and 5b rfb turns out to be these calculations write this on your paper
answers -1 28 over three -40 2.7 and of course you do if you do the definite integral that integrate thats exactly which can you can come up with your also pretty neat how every step calcaneus dot com go to my site by my program if you wanna past calculus and i subscribe if you want to see more videos have a good one

Trapezoidal Rule Solved on TI89

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Hello everyone this is Tom from everystepcalculus.com, everystepphysics.com. Programs that show you step by step how to do these problems. A student submitted this to Yahoo Yahoo and it was– you can see the problem, regarding the trapezoidal rule. And, let’s do it. Index 8 to get to my menu. I’m going to scroll up to get right to the bottom of the menu. Cause the trapezoidal rule, T, is closer to the W’s than the A’s. So I did it that way. There’s the trapezoidal rule there on the menu. And it’s really a trapezoidal rule calculator that’s really what would it involves, pretty neat, too. We add our function. You have to press alpha before you enter anything into these entry lines here in your calculator. Alpha X squared plus 4 times X. I always show you what you’ve entered, you can change it if you want. I say it’s okay, enter the range. The range is alpha 0 and alpha 4. Looks pretty good. Remember, that’s a definite integral, you can go to my definite integral program and do the calculation exactly. It’ll give you the same answer as what we’re gonna get here. This is a roundabout way of doing something that’s nonsense in both areas. So I say that’s okay. We’re gonna enter the intervals, which is alpha 4. And here’s the formula, change of X divided by 2, and then f(a), 2 of F of x1, 2 of F of x2, etcetera, etcetera. Down to f(b). This is the actual formula, no matter how many intervals. Change of x is B-minus a divided by n, so that’s 4 minus 0 divided by 4, turns out to be 1, and we compute the intervals.  x0, x1, x3, x4, here’s the answers: 1 and 2 and 3 and 4. and we replace them in the function. F(a) is 0, so we have 0 placed in the function, we’re substituting 0 for every X in the function. And the answer is this right here, 0. Do the same thing for f(x1) and f(x2). F(1) is placed into the function to equal 5, 12. F(x3) and f(b), so 21 and 32 answer. You’d put parenthesis around these quotation marks, the calculator makes me use quotation marks, but you’re gonna put parenthesis around these, okay, so you look good on your paper. So when we do the definite integral here you’re gonna do the trapezoidal rule approximation. There’s the approximation, and we substitute for these values here. Put this on your paper and just look like a genius. Do the calculations, comes up to this right here, that turns out to be 54 square units. Pretty neat, huh? Everystepcalculus.com, go to my site, buy my programs if you wanna pass calculus easy, and subscribe to me if you wanna see more videos and know how my programs work so great. Have a good one.

Simpsons Rule Test Question

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Go to our Simpson’s Rule page to see more info and many more step by step video tutorials for the TI-89.

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Hello everyone, this is Tom from everystepcalculus.com, everystepphysics.com. Calculus problem regarding a Simpsons rule test question and a quad root problem. Let’s do it. Index 8 to get to my menu. I’m gonna go up to get to the bottom of the alphabet to get to the S’s, where Simpson’s rule is in my menu. At the T’s now… There’s Simpsons. Gonna enter our function. You have to press Alpha before you enter anything into these entry lines here, alpha 2 times X to the 1 divided by 4. Looks like a good function, we’re gonna enter the range, Alpha 0, Alpha 8. Intervals we’re gonna enter as alpha 8. There’s the formula for Simpson’s rule. We do the change of X first, write this on your paper you’ll look like a genius. We do the intervals all the way up to 8, just like you see it here and then we place those into the function. Write down everything you see here on your paper, and so when we do the definite integral of 0 to 8 with this function and use the Simpson’s rule for approximation, here’s what you’re putting down on your paper. Don’t slop anything off of it. And then you substitute those values we got before, you add them up, and it comes to 63.5, and you multiply times one third. Here’s the answer. Pretty neat, huh? Everystepcalculus.com, go to my site, buy my programs, and pass calculus. Have a good one.

Graphing a parametric equation

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Hello everyone, this is Tom from everystepcalculus.com, everystepphysics.com. We’re gonna do a sketch by hand concerning parametric equations. A position formula for position vectors, and then eliminate the parameter. The parameter is T. So let’s do it. Index 8 to get to my menu. I’m already at sketch graph. Here’s the position in vector format. And you have to press alpha before you enter anything into these entry lines here. Alpha T squared minus 4, and alpha t divided by 2. If z is not given, enter 0. Alpha 0. I always show you what you’ve entered, you can change it if you want in my programs. And we’re gonna scroll down here to sketch by hand. I put in the arbitrary numbers for you that you’re gonna then work in the formula. Here’s the answer, you put these on a graph paper and you sketch the graph of this function. We’re gonna go back now and eliminate the parameter.
Of course you know how to do that, don’t you. It’s all nonsense if you ask me, calculus is nonsense. Eliminating parameter. Solve for t in the y equation, which we did here. t equals 2y, and then you put that in the x equations, into the x equation here. And here’s the answer: 4y squared minus 4. Sometimes your professor might want you to put it into a 0 format or an equal 0 format. You change, transpose, the x to the other side minus x, and then change the sign, x minus 4y squared plus 4 equals 0. Alright, pretty neat, huh? Everystepcalculus.com, go to my site, buy my program if you wanna pass calculus, and subscribe if you wanna see more videos that I might make. And don’t forget physics, either, okay? Have a good one.

Parametric Equations-Find Speed

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Find Speed

x=t^3-4*t

y=t^2+1

z=0

Raw Transcript

Hello everyone, Tom from everystepcalculus.com, everystepphysics.com, a problem dealing with parametric equations and the item of speed. So let’s do it! Index 8 to get to my menu, go to speed. Speed is a scaler, it has no direction, no angle, unless you add time to it, which I’ll show you in my program here. There’s speed, and write all this on your paper here, the r(t) formula is x(t)i, j, and k, and x, y, and z. And we have our functions for x and y. You have to press alpha before you enter anything into these entry lines here. Alpha… the problem is T cubed minus 4 times T. And Alpha T squared plus one. Looks like the “t” is missing. Here we go, put the “t” in. Here we go, and alpha 0 for the z component, or the K component if it’s not given. These are all set up problems, they don’t happen in real life,
which is nonsense for calculus. A lot of it is like that in calculus. So, I always show you what you’ve entered, you can change it if you want. Say it’s okay. And we’re gonna scroll down here to the calculation– you have different things on the menu that you can do with this entry of “t” variables. Speed, there it is there, and of course you write the derivative of the magnitude of it, which is actually the square of the derivatives. Calculus, the sudoku of math. X prime, here’s the derivatives of that and the magnitude is then the derivative squared. I’m going to say that the time was not given in this problem at first, so to do it we’re gonna go back, we’re gonna press number 2. And so speed is the square root of 3t squared plus 2t minus 4. We’re gonna go back and do it again. Add some time component. Press yes for time… add– yes, let’s put 7 seconds. And so, it’s t equals 7, you’re entering it into the variable of the function. You’re gonna put parenthesis around this “7” on your paper but I have to use quotation marks. Turns out to be that. Turns out to be 12.5 units per second. But, because “t” is given… “t” is given, so we do have an answer, it’s 1.4732, arc tangent of the rise over run.  Have a good one, everystepcalculus.com, go to my site, buy my program if you want to pass calculus easy, or subscribe and see other videos I might make. And don’t forget about physics either. Thanks so much. Have a good one.

 

TI-89 Calculus |Radius of a Sphere

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Find the radius of a sphere. Give two points on its circumference.

Points are P=(7, -2, -6) and Q= (5, -9, 4)

Raw Transcript

Hello everyone, Tom from everystepcalculus.com, everystepphysics.com. We’re gonna do a calculus three problem regarding a sphere. And we’re given two points on it’s circumference. Outer shell, you know. And let’s do it. Index 8 to get to my menu,
find the radius. Scroll up to get to the bottom of the alphabet, cause the sphere radius is in the S’s and closer to the W’s than the A’s. There’s sphere radius there. Choose that one. We’re gonna put our points in.You have to press alpha first. Alpha 7, Alpha minus 2. Alpha minus 6. Alpha 5 Alpha minus 9. Alpha 4. I always show you what you’ve entered, you can change it if you want. Looks okay. Now I’m gonna find the radius number 4. Here’s the formula. Write this stuff on your paper. And R equals these calculations here, just as if you did it yourself without mistakes. And the answer. Pretty neat, huh? Everystepcalculus.com, go to my site, buy my programs if you want to pass calculus, and subscribe if you want to see more videos from me. Have a good one.

Find the Standard Equation of a Sphere

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Find the standard equation of the sphere.

Let P1 = (-7, -9, 7) and P2 = (0, 1, 1) be endpoints of a diameter

Raw Transcript

Hello everyone, Tom from everystepcalculus.com, everystepphysics.com. A problem regarding a sphere and the standard equation a person submitted, and let me show you how I do it in my programs. Index 8 to get to my menu, my main menu. I’m gonna scroll up to get to the S’s at the bottom, it goes to the bottom of the alphabet so it’s easier and quicker to get there. You can press second and these cursors to go screen by screen on your calculator. Those are all the choices you have, and we’re gonna have sphere equation.
And we’re gonna enter our P, Q points. All professors do things different, which I’m against in calculus. Well, I’m not too thrilled about calculus at all. We have p1 and p2 here, in most cases it’s P and Q points. You have to press alpha before you enter anything in these entry lines here. Alpha, the first one is minus 7. There it is. Alpha minus 9. 7 is the P point. These are point on the outside of a sphere, and they give you two points are you’re supposed to find the radius. And different types of things. Not easy. Even if you know the formula it is not easy, you’re gonna mess up on the minus signs or whatever. That’s why the program steps up so you don’t mess up, and I didn’t mess up. The Q point is Alpha 0, Alpha 1. Alpha 1 for the Z point. I always show you what you’ve entered you can change it if you want. I say it looks pretty good. And we’re gonna choose equation, standard equation, number 5. There’s the formula. And you have to find the xo, yo, zo first Which is this system here. That equals this. Standard equation that is these entered into the equation. Here’s the standard equation. Pretty neat, huh? Everystepcalculus.com. Now I noticed, with the minus in minus, you might have to think in life a little bit, so you might have to say, oh there’s a minus and minus, minus times a minus is a plus. So you might put on your paper, x plus 7, over 2. Or same thing with y. Y equals minus, minus a minus, which is equal to a plus. Which would be y plus 4, and this would be z plus 4. So, keep that in mind. Have a good one. Everystepcalculus.com, go to my site, buy my program if you want to pass calculus. Subscribe if you want to see more movies from me. Thanks and have a good one.

Vector Function on TI-89 & Titanium

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Hello everyone, Tom from everystepcalculus.com everystepphysics.com, a quick example of
vector valued function, r(t) formula, or vector function. And with regard to speed. So, let’s do it. Index 8 to get to my menu. We’re gonna scroll up to get to the bottom of the menu so that we’re closer to the s section; it’s all alphabetical. I choose speed. Speed is a scaler, meaning it has no direction, it has magnitude, but no direction. Unless time is added to it, and then it does have a direction. You’re gonna enter these values here, but if Z is not given you’re gonna enter 0, okay? So, you have to press alpha before you enter anything in these entry lines here. Alpha minus 3 times T Alpha 2 times T Alpha minus 6 times T. I always show you what you’ve entered, you can change it if you want. There’s the vector. These indicate that it’s a vector, these arrows here. Say it’s okay. Now we’re gonna choose speed, we’re looking for speed. It’s right there. And it’s given by the magnitude. Magnitude is the derivative of the function times the squares of each one of them. So it’s X prime of t squared, y prime of t squared, z prime of t squared. And the derivatives are minus 3, 2, and minus 6. And we square them. Asks if there’s time given, I’d say there’s no time given in this one. So we’re gonna choose number 2. And then just square the values, sum them up,
49, and there’s the answer: 7 units per second. Pretty neat, huh? everystepcalculus.com, go to my site, buy my programs, and subscribe if you want to see other videos. Have a good one.

Find Midpoint of Sphere on TI-89

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Find the midpoint of a sphere.

Let P = )5, -2, 3) and Q = (0, 4, -3) the endpoints on the circumference sphere.

Raw Transcript

Hello again everybody this is Tom from everystepcalculus.com, everystepphysics.com.
We’re gonna do some calculations in a sphere. This is generally calculus three. And we’re gonna find the midpoint, or center, of a sphere. Index 8 to get to my menu. You can scroll up to get to the bottom of the menu so you can get to the S section quicker. You can press second and the cursor here to get screen by screen instead of one click like I’m doing. This is a simulator. Now we’re gonna choose here, center and midpoint. We’re gonna enter our P and Q points pressing Alpha first. Alpha 5. minus 2 Alpha 3 The Q point is Alpha 0, Alpha 4
Alpha minus 3. Now we gotta go back and change them. Alpha 5 Alpha minus 2 Alpha 3 Alpha 0 Alpha 4. And Alpha minus 3. I always show you what you’ve entered, you can change it if you want, which we just did. Say it’s okay. Now I’m gonna press number 1. Number 3 for midpoint Here’s the calculations: xo, yo, zo. And the answer. Everystepcalculus.com, go to my site buy my programs if you want to pass calculus.
And also subscribe so you can see other videos I might make. Hey have a good one.

Shell Method

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Raw Transcripts
Hello, everystepcalculus.com. A problem regarding Shell Method and the axis of rotation is vertical. A Yahoo problem. Let’s do it. Index 8to get to my menu. You need to get to the s’s of the alphabet so you have to go down to the bottom of the alphabet by going up and then clicking up to go to finding shell. And it is there. And we have the choice of horizontal axis or vertical axis, we want this problem is vertical axis. There’s the formula. And it’s taken me a long time to program this stuff, but if (p)x is the radius, if it’s not given enter x for p(x), okay, cause there’s two functions, p(x) and h(x). And sometimes it’s more elaborate than this one is. You have to press alpha before you enter anything into these entry lines so I’m gonna…. here’s p(x) here, alpha x I’m gonna enter. And for h(x) is the problem, alpha 6 minus x. 1Oops. 6 minus X. I always show you what you’ve entered you can change it if you want, that’s okay, now, I press number one. One of the tough things about shell is the confusion of the whole thing, and the nonsense of the whole thing, but then we’re gonna find the A&B limits. You do that by– if nothing else is given for the x value, than the x is equal to 0 because you got a vertical axis of revolution. It’s vertical, and we set the X at equals zero point. So we set the equation equal to that. 0 equals 6 minus x, we get the limits, it’s six. This is where the function crosses the x-axis. So, here’s the equation now for the integral. And so we have this issue. Mark this on your paper.
When we do the integration, here’s the integration of the function. And, as we substitute at x equals 6, the limits, it’s 72 pi and x=0,. we get 0. Upper limit minus lower is 72 pi.Have a good one.

Integral Calculator With Steps

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Raw Transcripts
Hello, everyone. This is Tom from everystepcalculus.com. There’s been many, there’s always requests for Integral Calculator with Steps and that’s exactly what my programs do. And Integration is one of the toughest things in Calculus. It was for me when I was in class. I hated Calculus. You probably feel the same way and I’ve found nobody that likes Calculus. Except maybe Professors. But anyways, I’m going to show you how my programs work on U Substitution. Index 8 to get to my menu. I’m already at U Substitution. I have scrolled there. We’re going to enter our function. You have to press Alpha before you enter anything into these entry lines, here. Alpha 6 times x to the fourth power times the quantity parentheses 3 times x to the fifth power plus 2, close off the parentheses to the sixth power. I always show you what you’ve entered. 6x 4 times 3 x quantative to the 5 plus 2 to 6. Looks
good to me. I say it’s okay. And we’re going to work the problem. Busy means the program is loading. We’re going to evaluate this. First we rewrite it where all constants come out of the integral. And then we put the x to the 4. The way that you know that any problem is U Substitution is that you look immediately at what’s inside the parentheses. You take the derivative, right now you should be able to do, this is 15x to the 4. Right now in one second, you should be able to know the derivative of that. And you notice that x4 is on the outside, too. If it isn’t, it’s not a U Substitution problem. It has to be converted, okay. So I do all that for you, really. But that you have some understanding of how you do U Substitution. U is equal to this, du is equal to this and then we make this the other trick, this whole system here took me about a year to figure this out in a system that works, you know. And so, this always has to be x to the 4 dx over here so you have to take the 15 and divide the du by that on the other side using Algebra, of course. And so it works the problem. 6, you take of course the du with the 6 here, you have a du with a 15 notice the 15 come out of the, here’s the constant again so that comes out of the integral and goes in front right here, see it right here. 6 times that, of course, with the 2 fifths. etc, etc. Here’s the answer to your problem right here. Have a good one. everystepcalculus.com

ln(x) Integration

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Raw Transcripts

Hello, everyone. This is Tom from everystepcalculus.com, everystepphysics.com. I’m going to do a integral of a natural log in this video to go with my menu. Let’s do an index 8 to get to my menu. I’m already at LN of X integral, which is natural log of you know, and integrate that. We’re going to press number 2, integration. And we’re going to integrate transcendentals. Number 1, log of X. And you have to press alpha before you enter anything in these entry lines here. And we’re going to enter the function that you see. Alpha 2nd log of 5 times X. It will show you what you’ve entered; you can change it if you want. I say it’s okay. I’m going to rewrite this. Like you see, integral of log of 5x and then we have the 1 over here, DX, to show you that we’re going to do DV is equal to 1, V is equal to the interval of 1dx. The answer is X. And then U is log of 5x, but that always equals the derivative of that is one over X. Here’s the formula: VU minus the integral of VDU. And we plug in the variables for the formula. Here’s V and here’s U, minus the integral of V again and then DU. And then we’re going to integrate 1 here, because that’s what that works out to, what we just put down before. And so the integration of integral of 1 is minus X. So here’s the answer: X times log of 5 times X minus 1 plus C. Notice we’ve factored the X out here. Also notice that sometimes‚ you might think about this too‚ log of 5 times X is really log of 5 plus log of X, so that could be written like that, too. X times log of 5 times log of X minus 1 plus C. So subscribe at my site and you can see more movies that I might make for your enjoyment. Have a good one.

Line Integral

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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.

Antiderivative Calculator

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Find the Antiderivative of:  √(6x-1)

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Hello again everyone, this is Tom from everystepcalculus.com, everystepphysics.com, I’m gonna show you how to turn your titanium calculator with my programs into a antiderivative calculator. Okay, so, index 8 to get to my menu. I’m gonna do a U substitution, because most problems are U substitution integration and antiderivative is really doing the integral of a derivative. Where as an integral itself is doing an integral of a function which might be a derivative or not. But antiderivative is really an integral, and it’s an indefinite integral because you have to have a plus C at the end and somebody has to decide on the C, there’s 10 million integrals for an indefinite integral, all decided by what the plus C is. Who decides that, I have no idea. U substitution, enter a function, you have to press alpha before you enter anything into these entry lines here, don’t forget that. Alpha and the square root second square root. And the square root of 6 times X minus 1. Close off the parenthesis. Oh, didn’t press alpha I guess. 6 times x minus 1. That’s better. Now we show you what you’ve entered, you can change it if you want. Say it’s okay. And we’re into the problem. U is whatever’s in the parenthesis, you should be able to do the derivative of whatever’s in here in a second okay, in your sleep– for instance, the derivative of 6x is 6. Well here you have U of 6x minus 1, and the derivative is 6dx. We want to always have the dx by itself, because the dx is by itself up here, right. So you’re gonna take this and use algebra, and bring it over to the other side, and divide du by 6. That equals (1)dx over here. So now, the square root of u then is equal to the square root of 6x minus 1 because we made this u. So that equals the integral of u to the one half, because if this was a cube root it would be one third, if this was the fifth root it’d be one fifth here. But this is the square root, so it’s the one half. And then you have to add the du divided by 6, which we formulated before. That’s one of the big tricks in u substitution that took me 10 years to figure it out. So we have to bring all constants out of the integral, which we do here, one sixth here, we add 1 to the 1/2 here, which becomes 3, 3 halves, divided by 3 halves, so you have one sixth when you divide by a fraction, you invert multiply, so we inverted the fraction. Two thirds. And the answer’s 1/9th, 6 to that. Pretty neat, huh? Everystepcalculus.com, go to my site, buy my program if you want to pass calculus and do your homework. Have a good one!

Step by Step Calculus Solver

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Step by Step Calculus Solver

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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.