Question

Find the mass of the lamina described by the inequalities given that its density is p(x,y)=xy.

x>= 0, 3 <= y <= 3+(9-x^2)^square root

Answer 1

The problem also said that polar coordinates could be used to simplify. I just need someone to check to make sure I'm getting the correct limits, as I'm converting..

Answer 2

\[x \ge0,3 \le y \le 3+\sqrt{9-x^2}\]
^ this is the original problem

Answer 3

\[\int\limits_{0}^{x}\int\limits_{3}^{3+\sqrt{9-x^2}}(xy)dydx\]

Answer 4

I know by converting to polar coords one of my r limits is 6 and the other 3, would theta be 0 and pi/2?

Answer 5

this is the graph I got for 3+\[\sqrt{9-x^2}\]