## anonymous 5 years ago Consider the given curves to do the following. y=x^3 y=0 x=1 Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about y = 1.

1. dumbcow

A(y)= 2*pi*y*(1-y^1/3) $V = 2\pi \int\limits_{0}^{1}y(1-\sqrt[3]{y}) dy$ $=2\pi \int\limits_{0}^{1}y - y ^{4/3} dy$ $=2\pi [\frac{1}{2}y ^{2} - \frac{3}{7}y ^{7/3}]$ $=\frac{\pi}{7}$

2. anonymous

ahh posted in wrong question lol