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)=x^2/2, y=0, x=0, x=4.

Answer 1

`51.2\pi`

Explanation:

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

So, we will use integral to calculate the volume.

`V = \pi\int\limits^4_0 ((x^2)/(2))^2dx =\pi\int\limits^4_0 (x^4)/(4)dx =\pi(x^5)/(20)|^4_0=51.2\pi`