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

Multiple Choice

Using a change of variables, the double integral $\iint$ _{R $( x + y ) e ^ { x - y } d A$} where R is the region bounded by the quadrilateral with vertices (4, 0) , (6, 2) , (4, 4) , and (2, 2) is

A) $12 \left( e ^ { 2 } - 1 \right)$
B) $- 12 \left( e ^ { 4 } + 1 \right)$
C) $- 12 \left( e ^ { 4 } - 1 \right)$
D) $12 \left( e ^ { 4 } - 1 \right)$
E) $12 \left( e ^ { 4 } + 1 \right)$