Question

Reversing the order of integration?

Answer 1

\[\int\limits_{0}^{1}\int\limits_{-\sqrt{1-y ^{2}}}^{\sqrt{1-y ^{2}}}x ^{2}y dxdy\]

Answer 2

actually looks like an integral that would be much more easy to solve in polar coordinates, but I guess that's not what you're supposed to do, can you draw the Region R?

It seems to be a circle of radius 1 to me, centered at the origin.

Answer 3

what would be the x limits and y limits of this circle in integration using x as constant?