Evaluate the Integral $\iint _ { R } \frac { x ^ { 2 } } { x ^ { 2 } + y ^ { 2 } } d A$

Short Answer

Evaluate the integral $\iint _ { R } \frac { x ^ { 2 } } { x ^ { 2 } + y ^ { 2 } } d A$ , where $R$ is the annular region bounded by the circles $x ^ { 2 } + y ^ { 2 } = 9$ and $x ^ { 2 } + y ^ { 2 } = 16$ , by changing to polar coordinates.