Question

Find the volume of the solid of revolution formed by rotating about the x--axis the region bounded by the given curves.

f(x)=2ex, y=0, x=-2, x=1.

Answer 1

`2\pi(e^2-e^(-4))`

Explanation:

We are given:
`f(x)=2e^x`

So, the integral will be used to calculate the volume.

`V = \pi\int\limits^1_(-2)(2e^x)^2dx=\pi\int\limits^1_(-2)4e^(2x)dx=2\pi e^(2x)|^1_(-2) =2\pi(e^2-e^(-4))`