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?
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?
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 $b=3$.