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

Essay

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