Evaluate the given integral by making an appropriate change of variables. 7 x − 4y 7x − y da, r where r is the parallelogram enclosed by the lines x − 4y = 0, x − 4y = 5, 7x − y = 1, and 7x − y = 4

The obvious substitution is

so that the limits of integration in the -plane are constant.

We can solve the above system for to get

The Jacobian for this change of coordiantes is

so that the differential becomes

Now,

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step-by-step explanation: