Question

Use the solid obtained by rotating the region bounded by y=x^2 and y=9 about the x-axis (using the disk method).

Answer 1

To find the volume you use the formula:
\[V= \int\limits_{a}^{b}\pi \left[ f(x) \right]^{2}dx\]

You have a region bounded by y=x^2 and y=9. To find the upper and lower limits of integration we have to check where the function y=x^2 and the line (and function) y=9.
We do this by setting both equal to eachother, that is y=y --> x^2=9.
This gives us that x=-3 and x=3, thus we have the limits of integration.

\[V=\pi \int\limits_{-3}^{3}\left[ x^2 \right]^2dx\]

Now it's just a "regular" integral to solve...