Use Polar Coordinates to Combine the Sum Into One Double Integral

question 2

Essay

Use polar coordinates to combine the sum $\int _ { \sqrt { 2 } } ^ { 2 } \int _ { \sqrt { 4 - x ^ { 2 } } } ^ { x } x y d y d x + \int _ { 2 } ^ { 2 \sqrt { 2 } } \int _ { 0 } ^ { x } x y d y d x + \int _ { 2 \sqrt { 2 } } ^ { 4 } \int _ { 0 } ^ { \sqrt { 16 - x ^ { 2 } } } x y d y d x$ into one double integral. Then evaluate the integral.

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