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Use the given transformation to evaluate the integral.

Use the given transformation to evaluate the integral.

Double integral (5x+15y)dA, where R is the parallelogram with vertices (−2, 8), (2, −8), (3, −7), and (−1, 9);
x=1/5(u+v), y=1/5(v-4u)

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change of variable and surface integral.docx

Observe that
On solving,
This means, u varies between – 10 and 10.
Similarly,
Also,
Put the 4 coordinates together, we confirm that v varies between 0 and 5.
Using these limits, the required...

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