Double/Triple/Iterated Integrals and Max/Min

[SomeGuy]

Hi people, I have a midterm for calculus coming up, so I was wondering if you guys could give me some interesting problems regarding double/triple/iterated integrals with change of variables, and max/min.

 

[Mindscrape]

1) Find the ratio H/R of height to radius to minimize the total surface area of a right-circular cylinder of fixed volume V.

2) Find the integral $$I = \iint_R 21y dx dy$$ where R is the region above the x-axis and bounded by $$y^2 = 4 -4x$$ and $$y^2 = 4 +4x$$. (I would use a jacobian.)