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)=ex, y=0, x=0, x=2.

Answer 1

`(\pi)/(2) (e^4-1)`

Explanation:

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

The volume will be calculated via the integral as follows,

`V=\pi\int\limits^2_0(e^x)^2dx=\pi\int\limits^2_0e^(2x)dx=\pi (e^(2x))/(2) |^2_0 = (\pi)/(2)  (e^4-e^0)=(\pi)/(2) (e^4-1)`