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

question 73

Multiple Choice

Use the given transformation to evaluate the integral.
- $$\begin{array} { l } \mathrm { u } = - 6 \mathrm { x } + \mathrm { y } , \mathrm { v } = 4 \mathrm { x } + \mathrm { y } ; \\\quad \int _ { \mathrm { R } } \int ( \mathrm { y } - 6 \mathrm { x } ) ( 4 \mathrm { x } + \mathrm { y } ) \mathrm { dxdy } ,\end{array}$$
where $R$ is the parallelogram bounded by the lines $y = 6 x + 5 , y = 6 x + 9 , y = - 4 x + 3 , y = - 4 x + 10$

• A) \(\frac { 637 } { 5 }\)
• B) \(\frac { 1274 } { 5 }\)
• C) 25,480
• D) 12,740

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