How do you change a Cartesian integral into an equivalent polar integral?

Question

For Example:
The double integral of xy^2dxdy
E={x,y| 2<_y<_0, 0<_x<_-sqt(1-(y-1)^2)
Any ideas?

Answer 1

Hello

Since x = rcos(theta) y = rSin(theta) and x^2 + y^2 = r^2

Make your substitutions.

rcos(theta) * (rsin(theta))^2

Take it from there.

Hope This Helps!