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## Calculating Integral with Shell Method

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## Related Rates – Pulley Rope

### 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?

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## 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)?

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## Simpsons Rule on TI89

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

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## Trapezoidal Rule Solved on TI89

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## Simpsons Rule Test Question

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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## Graphing a parametric equation

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## Parametric Equations-Find Speed

### Find Speed

### x=t^3-4*t

### y=t^2+1

### z=0

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## TI-89 Calculus |Radius of a Sphere

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

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

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## Find the Standard Equation of a Sphere

### Find the standard equation of the sphere.

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

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## Vector Function on TI-89 & Titanium

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## Find Midpoint of Sphere on TI-89

### Find the midpoint of a sphere.

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

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## Shell Method

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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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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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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

### Find the Antiderivative of: √(6x-1)

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## Difference Quotient Solver

## Difference Quotient Solver

## Step by Step Calculus Solver

## 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.

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