I don't feel very confident with this concept.
Suppose R is the region bounded by y = x2, x = 2, and y = 0
1) Find the volume of a solid that is generated by revolving R about the x-axis. - I believe I did this one correctly, but I want to be sure. I got 32pi/5.
2) (same) ... revolving R about the y-axis. - I feel the same about this one. I got 8pi.
3) ... revolving R about y = -3.
4) ... revolving R about x = 3.
For 3 and 4, I've tried setting up the integrals a few different ways, but I don't think any of them are right.
If someone could help me set these up or give me some tips & verify that the first two are correct, I'd be eternally grateful.