How good are YOU at calculus?

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16 years ago 10/29/2007 1:00am EDT

So I'm reviewing for an exam that I have tomorrow, and I came across these two similar problems. I realized I completely forgot how to do them. I know they both have to do with the integral of pi R squared, and something to do with outter radius - inner radius, but I am drawing a blank on how exactly to do them. Probably due to cramming, but somebody help me out with these please ---

1. Find the volume of the solid generated by rotating the region bounded by the curves y=xx and x=yy about the y-axis.

2. Find the volume of the solid generated by rotating the region bounded by the curves y=3x-xx and y=0 about the line x= -1.

Again, just trying to figure out how to do these problems. Since I'm reviewing for an exam, the process is much more important than the raw answer.

16 years ago 10/29/2007 2:35am EDT

re: mystertree

16 years ago 10/29/2007 2:39am EDT

re: mystertree

you wont find any better results at dyestat.

http://talk.dyestat.com/showthread.php?p=2156307#post2156307

16 years ago 10/29/2007 2:44am EDT

re: turtleboats

Cylindrical coordinates... Start by thinking of it as a bunch of circular slices of different radii.

16 years ago 10/29/2007 2:47am EDT

re: rgtegfd

rgtegfd wrote:
Cylindrical coordinates... Start by thinking of it as a bunch of circular slices of different radii.

cylindrical what the @!? the only math i know is

whats an owls favorite math subject

owlgebra

16 years ago 10/29/2007 2:53am EDT

re: mystertree

thanks for the help quenton..

16 years ago 10/29/2007 7:57am EDT

re: mystertree

16 years ago 10/29/2007 8:07am EDT

re: mystertree

If you don't have Stewart's text, go find a copy. Should explain everything clearly. Some online sites should also explain. Search for "solids of revolution."

16 years ago 10/29/2007 8:54am EDT

re: kartelite

A text-based message board is not the place to ask. With paper & pencil this would take less than a minute to explain in a way that's very easy to retain.

The formula is pi times the integral of [f(x)]^2*dx (think pi*[r squared]). Your limits of integration are the points of intersection of the two functions given.

16 years ago 10/29/2007 9:03am EDT

re: jsquire

16 years ago 10/29/2007 9:24am EDT

re: mystertree

If you don't understand cylindrical coordinates and your exam is tomorrow, you're probably SOL.

Call up someone in your class to study with.

16 years ago 10/29/2007 9:56am EDT

re: mystertree

Well for the first one both y=xx and x=yy start at the origin.

y=xx curves upwards slowely at first then quicky as it is a squared function.

x=yy is the inverse of y=xx. It flattens out.

Both of these together should form a shape that looks like an eye. The inner radius would be the x=yy and the outer funcion would be the y=xx funcion. THis is because the x=yy is closer to the y axis. Find the volume of each individually then subtract. Use the intersection points when intergrating. I think most of this is correct even though it's been a few months since I've done much Calc (or any math really)

The second one is moe compicated but same general principles-just remember to rotate around the line x=-1, not x=0

16 years ago 10/29/2007 10:09am EDT

re: mystertree

For the first one...

It' x=yy I think by that you mean x=y^2 which is the same as y=x^(1/2)

The two curves will be equal when x=0 and x=1. y=x^(1/2) will be on top. The integral you want to take is from 0 to 1 of

2(pi)x(x^(1/2)-x^2)dx

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