Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis.
y = x3, y = 8, x = 0; about x = 5

We seem to be getting it wrong on webassign but can't figure out any other way to do it. Here's what we did: (if you could explain it to us, even better!)

integral from 0 to 8 of (2pi (y^4 /3 - 5y^1/3))

https://www.wolframalpha.com/input/?i=area%20bounded%20by%20y%20=%20x3,%20y%20=%208,%20x%20=%200%20rotated%20about%20x%20=%205

Wolframalpha integrates with x not y, so maybe try it that way and then check your answer vs theirs (504pi/5)

This post was edited by Dontrunaway on May 14 2016 11:55am

For the y = x^3, you need to write it in terms of y since the integral is in terms of y and since it is being rotated about a vertical line. [x = y^(1/3)]

The general form for the Volume of a rotated shell is the Integral from a to b of (pi (Router^2 - Rinner^2)). Since pi is a constant it can be pulled out. The outer radius in this occasion is 5. This inner radius as x and summarily y increase is 5 - y^(1/3).

So the volume V = pi * Integral from 0 to 8 of [5^2 - (5 - y^(1/3))^2] dy



E/ sorry mine is disk/washer method.

This post was edited by timmayX on May 15 2016 01:20am

Try rotating the cylindre on an ovale tan the 0 is a trick question cause value is 1 on a grid