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)=2/√x+2, y=0, x=-1, x=2.

Answer 1

`4\pi\ln4`

Explanation:

We are given:
`f(x)=(2)/(√(x+2))`

The volume will be calculated with integral.

`V = \pi\int\limits^2_(-1)(f(x))^2dx=\pi\int\limits^2_(-1)(4)/(x+2)dx=4\pi\ln(x+2)|^2_(-1)=4\pi\ln4`