Question

In Exercise use the integration feature on a graphing calculator to find the volume of the solid of revolution by rotating about the x-axis each region bounded by the given curves.

f(x)=1/4x^2, y=0, x=-2, x=2.

Answer 1

`(4\pi)/(5)`

Explanation:

We will use the following property of integral to calculate the volume of the solid of revolution by rotating about the x-axis:

`V=\pi\int\limits^2_(-2) ((1)/(4)x^2)^2\:dx=\pi\int\limits^2_(-2) (1)/(16)x^4\:dx=\pi(x^5)/(80) |^2_(-2)=(4\pi)/(5)`