Question

Refer to the figure and find the volume V generated by rotating the given region about the specified line.
a = 2
b = 3
ℛ1 about AB

Answer 1

Do you have an idea on how to start?

Answer 2

The shell method will be slightly less work here.

So you can compute the volume with
\[V=2\pi\int_0^1\underbrace{(1-x)}_{\text{radius}}\underbrace{ax^b}_{\text{height}}\,\mathrm{d}x\]