Thread: Help with finding volumes of rotated curves

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 the x-axis.
Find the volume V of this solid.

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



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

1) I always try to do it both ways, just to emphasize the concepts in my mind.

2) That is not . Please demonstrate your work.

3) You have it set up exactly correctly. Try the integral again.

4) And the other way: . See if you get the same answer.

5) Please learn to observe an exploit symmetries. The limits of your integral could have been [0,2] with the result multiplied by 2.

Thank you for the helpful reply i see what i did, or rather, didn't do.