Question

How do I find the volume of the solid obtained by rotating about the x-axis the region enclosed by the curves?

Find the volume of the solid obtained by rotating about the x-axis the region enclosed by the curves `y=(4)/(x^2+4)`, y=0, x=0, and x=2.

Answer 1

The volume is `4.038` cubic units.

Explanation:

Recall the formula for volume around the x-axis:

`V = piint_a^b y^2 dx`

Thus

`V = pi int_0^2 (4/(x^2 + 4))^2`

`V = pi int_0^2 16/(x^2 + 4)^2dx`

This is a pretty complex integral so you can probably evaluate by calculator. Doing this should get you

`V = 4.038` cubic units.

Hopefully this helps!