Rewrite the Integral $\int _ { - 1 } ^ { 1 } \int _ { 0 } ^ { \sqrt { 1 - y ^ { 2 } } } x d x d y$

Essay

Rewrite the integral $\int _ { - 1 } ^ { 1 } \int _ { 0 } ^ { \sqrt { 1 - y ^ { 2 } } } x d x d y$ in terms of polar coordinates, then evaluate the integral.