Question

Consider the given curves to do the following
x=4sqrt(y)
x=0
y=1
Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the x-axis.

Answer 1

A(y) = 2pi*y*(4sqrt(y))
\[V=2\pi \int\limits_{0}^{1}4y \sqrt{y} dy\]
\[=8\pi \int\limits_{0}^{1} y ^{3/2} dy\]
\[=\frac{16}{5}\pi\]