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The region bounded by the hyperbola $x^2 - y^2=1$, the line $y=-2$ , and $y=3$ is rotated about the $y$-axis. Find the volume of the resulting solid.

Can someone point me on how to set up the equation?

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Whoops double integral sry! –  Rustyn Dec 23 '12 at 7:53
    
No double integral needed for a solid rotated about a coordinate axis, see below. –  Ron Gordon Dec 23 '12 at 8:47
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1 Answer

For a solid generated by rotating a function $x(y)$ rotated about the $y$-axis, the volume of that solid between $y=a$ and $y=b$ is given by

$$\pi \int_a^b dy \: x(y)^2 $$

In your case, $x(y) = \pm \sqrt{1+y^2}$, $a=-2$, and $b=3$.

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