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

question 411

Multiple Choice

Use the given transformation to evaluate the integral.
- $$\begin{array} { l } u = y - x , v = y + x \\\quad \iint \cos \left( \frac { y - x } { y + x } \right) d x d y ,\end{array}$$
where $R$ is the trapezoid with vertices at $( 3,0 ) , ( 10,0 ) , ( 0,3 ) , ( 0,10 )$

• A) \(\frac { 91 } { 4 } \sin 2\)
• B) \(\frac { 91 } { 2 } \sin 2\)
• C) \(\frac { 91 } { 4 } \sin 1\)
• D) \(\frac { 91 } { 2 } \sin 1\)

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The ability of a species to continue existence and avoid extinction by adapting to environmental changes or overcoming threats.

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