Use the Given Transformation to Evaluate the Integral $$\begin{array} { l } u = y - x , v = y + x ; \\\quad \iint \cosh \left( \frac { y - x } { y + x } \right) d x d y\end{array}$$

Multiple Choice

Use the given transformation to evaluate the integral.
- $$\begin{array} { l } u = y - x , v = y + x ; \\\quad \iint \cosh \left( \frac { y - x } { y + x } \right) d x d y\end{array}$$
where $R$ is the trapezoid with vertices at $( 6,0 ) , ( 7,0 ) , ( 0,6 ) , ( 0,7 )$

A) $\frac { 13 \left( e ^ { 2 } - 1 \right) } { 6 e }$
B) $\frac { 13 \left( \mathrm { e } ^ { 2 } - 1 \right) } { 3 \mathrm { e } }$
C) $\frac { 13 \left( \mathrm { e } ^ { 2 } - 1 \right) } { 4 \mathrm { e } }$
D) $\frac { 13 \left( \mathrm { e } ^ { 2 } - 1 \right) } { 2 \mathrm { e } }$