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Evaluate the double integrals in Exercises 39–48. Use suitable transformations as necessary.

R(3x2-5xy-2y2)dA, where R is the parallelogram from Exercise 41

Short Answer

Expert verified

R(3x2-5xy-2y2)dA=-3434

Step by step solution

01

Draw the region

Step 1: Draw the region


Plot the given points to form the region and name the vertices.



Consider the new set of variables defined as,

u=x-2yv=3x+y


From the above equations,

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Plot these limits on u v plane,



02

Find the integral

Use the antiderivative to evaluate all integrals,

R(3x2-5xy-2y2)dA=72-70udu=72u22-70=72-722=-3434

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