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
Gió
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!):
enter image source here
The volume is then:
V=int_(-2)^(+2)pi(7-x^2)^2dx=
=piint_(-2)^(+2)(49-14x^2+x^4)dx=
=pi[49x-14x^3/3+x^5/5]_(-2)^(+2)=134.13pi

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