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Archives for June 2015
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
Trapezoidal Rule solved on TI-89 calculator.
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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