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Chapter 13: Q. 42 (page 1079)

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

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

Short Answer

Expert verified

鈭�鈭�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,

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

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Most popular questions from this chapter

In Exercises 57鈥�60, let R be the rectangular solid defined by

R = {(x, y, z) | 0 鈮� x 鈮� 4, 0 鈮� y 鈮� 3, 0 鈮� z 鈮� 2}.

Assuming that the density at each point in R is proportional to the distance of the point from the xy-plane, find the moment of inertia about the x-axis and the radius of gyration about the x-axis.

Evaluate each of the double integrals in Exercises37-54as iterated integrals.

localid="1650380493598" 鈭�鈭�Rsin2x+ydA,

wherelocalid="1650380496793" R=x,y|0鈮�x鈮�蟺2and0鈮�y鈮�蟺2

Evaluate each of the double integrals in Exercises 37-54as iterated integrals.

role="math" localid="1650327788023" 鈭�鈭�RysinxdA,

whererole="math" localid="1650327080219" R=x,y|0鈮�x鈮�蟺2and0鈮�y鈮�1

Evaluate the iterated integral :

鈭�01鈥�鈭�24鈥�鈭�鈭�15鈥�x+yz2dxdydz

State Fubini's theorem.
See all solutions

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