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Use the Given Transformation to Evaluate the Integral u=x+y,v=2x+y;R2(3x+4y)dxdy\begin{array} { l } u = x + y , v = - 2 x + y ; \\\quad \int _ { R } \int _ { 2 } ( - 3 x + 4 y ) d x d y\end{array}

question 270

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Use the given transformation to evaluate the integral.
- u=x+y,v=2x+y;R2(3x+4y) dxdy\begin{array} { l } u = x + y , v = - 2 x + y ; \\\quad \int _ { R } \int _ { 2 } ( - 3 x + 4 y ) d x d y\end{array}
where RR is the parallelogram bounded by the lines y=x+1y = - x + 1 , y=x+4,y=2x+2,y=2x+5y = - x + 4 , y = 2 x + 2 , y = 2 x + 5


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