Change to polar coordinates and integrate

[ahmetbaba]

Homework Statement

evaluate the iterated integral by converting to polar coordinates

integral, integral x²dxdy, the limits are 4 to 0 for the outer integral, and /sqrt(4y-y²) to 0 for the inner integral.

Homework Equations

The Attempt at a Solution

well x=rcos(/theta) so x² = (rcos(/theta))²,

however I have trouble converting the limits to polar coordinates here, I think the outer integrals limits here are from /pi/2 to 0 , and the inner integrals limits are from 1 to 0.

Is this set up correct so far?

So I have, integral, integral r²cos(/theta)² limits from /pi/2 to 0, and 1 to 0

 

[Mark44]

Homework Statement

evaluate the iterated integral by converting to polar coordinates

integral, integral x²dxdy, the limits are 4 to 0 for the outer integral, and /sqrt(4y-y²) to 0 for the inner integral.

Homework Equations

The Attempt at a Solution

well x=rcos(/theta) so x² = (rcos(/theta))²,

however I have trouble converting the limits to polar coordinates here, I think the outer integrals limits here are from /pi/2 to 0 , and the inner integrals limits are from 1 to 0.

I don't think so. The region over which integration takes place is a simple geometric shape. What is it?

Is this set up correct so far?

So I have, integral, integral r²cos(/theta)² limits from /pi/2 to 0, and 1 to 0