Use the Given Transformation to Evaluate the Integral Where $R$ Is the Parallelogram Bounded by the Lines

Multiple Choice

Use the given transformation to evaluate the integral.
- $$\begin{array} { l } \mathrm { u } = \mathrm { x } + \mathrm { y } , \mathrm { v } = \mathrm { x } - \mathrm { y } ; \\\quad \int _ { \mathrm { R } } \int ^ { \mathrm { s } } ( \mathrm { x } + \mathrm { y } ) \sin ( \mathrm { x } - \mathrm { y } ) \mathrm { dx } \mathrm { dy } ,\end{array}$$
where $R$ is the parallelogram bounded by the lines $y = x , y = x - 9 , y = - x , y = - x + 4$

A) 8(1 - cos 9)
B) 4(1 - cos 9)
C) 8(1 + cos 9)
D) 4(1 + cos 9)