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, y=0, x=0, x=3.

Answer 1

`9\pi`

Explanation:

We are given: f(x) = x.

We will use the volume integral property to solve the appropriate integral and find the value of volume.

`V = \pi\int\limits^3_0(f(x))^2dx = \pi\int\limits^3_0x^2dx = \pi(x^3)/(3) |^3_0=9\pi`