Hello again. I am going over a test review and had a few more problems. The first question, I can do the spherical conversion with no problems, but I'm just having a hard time visualizing and doing rectangular.

The second question is a Green's Theorem problem. Using the theorem the integral becomes very very simple (1-x). Our professor actually did this problem in class--and switched to a polar coordinate system. At this point he introduced a rule/trick/something? playing on even and odd values of n that made the integration of sin^n and cos^n simple. I have some jumbled notes, but can't really connect the dots so I can reproduce what was done. Anyway I'm rambling and being vague so I understand if this doesn't make any sense.