Question

The region bounded by y=e^(2x), y=0, x=-2, x=-1 is rotated around the x-axis. Find the volume.

Answer 1

you can use the shell method or the disk method... any preference?

Answer 2

\[V=\pi\int\limits_{-2}^{-1}f^2(x)dx=\pi\int\limits_{-2}^{-1}e^{4x}dx=\frac{\pi}{4}e^{4x}|_{-2}^{-1}=\frac{\pi}{4}(e^{-4}-e^{-8})\]