# How do you find the volume of the region bounded by y=7-x^2, x=-2, x=2 and the x-axis that is rotated about the x-axis?

##### 1 Answer
Mar 10, 2015

You can see that your solid looks like a football ball with cut ends (even if my graph is a bit crappy!):

The volume is then:
$V = {\int}_{- 2}^{+ 2} \pi {\left(7 - {x}^{2}\right)}^{2} \mathrm{dx} =$
$= \pi {\int}_{- 2}^{+ 2} \left(49 - 14 {x}^{2} + {x}^{4}\right) \mathrm{dx} =$
$= \pi {\left[49 x - 14 {x}^{3} / 3 + {x}^{5} / 5\right]}_{- 2}^{+ 2} = 134.13 \pi$