Using a Change of Variables, the Double Integral $\iint$ _{R $( x + y ) ^ { 2 } \sin ^ { 2 } ( x - y ) d A$}

Multiple Choice

Using a change of variables, the double integral $\iint$ _{R $( x + y ) ^ { 2 } \sin ^ { 2 } ( x - y ) d A$} where R is region bounded by the quadrilateral with vertices $( \pi , 0 ) , \left( \frac { 3 \pi } { 2 } , \frac { \pi } { 2 } \right) , ( \pi , \pi )$ and $\left( \frac { \pi } { 2 } , \frac { \pi } { 2 } \right)$ is

A) $- \frac { 7 \pi ^ { 4 } } { 12 }$
B) $\frac { 7 \pi ^ { 4 } } { 12 }$
C) $\frac { 5 \pi ^ { 4 } } { 12 }$
D) $- \frac { 5 \pi ^ { 4 } } { 12 }$
E) $- \frac { 11 \pi ^ { 4 } } { 12 }$