Hey I was recently introduced to the disc, cylindrical shell, and washer methods and I don't understand them fully mostly because it's difficult for me to imagine the shapes created when rotating curves and i dont know which method to use. Here is the problem:

Consider the solid obtained by rotating the region bounded by the given curves about thex-axis.

Find the volumeVof this solid.

I decided to use the disc method and set up my integral like so:

$\displaystyle \pi\int(16-4x^2)^2dx$

With -2 and 2 for the limits of integration...solving this yields 64$\displaystyle \pi$ but i cant get the correct volume.