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Chapter 13: Q. 40 (page 1079)

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

鈭�鈭�RxydA, where R is the parallelogram with vertices (0, 0), (3, 0), (5, 2), and (2, 2).

Short Answer

Expert verified

鈭�鈭�RxydA=17

Step by step solution

01

Draw the region

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

In the region R, the equations of boundary curves are,

AB:y=0BC:x-y=3CD:y=2DA:x-y=0

Consider the new set of variables defined as,

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Add the above equations,

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Most popular questions from this chapter

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

Describe the three-dimensional region expressed in each iterated integral:

鈭�鈭�24鈥�鈭�26鈥�鈭�05鈥�f(x,y,z)dydxdz

Find the masses of the solids described in Exercises 53鈥�56.

The solid bounded above by the paraboloid with equation z=8-x2-y2and bounded below by the rectangle R={(x,y,0)|1鈮�x鈮�2and0鈮�y鈮�2}in the xy-plane if the density at each point is proportional to the square of the distance of the point from the origin.

Evaluate the sums in Exercises 23鈥�28.

鈭�j=1m鈭�k=1n(j-k)

Evaluate each of the double integral in the exercise 37-54 as iterated integrals

鈭�鈭�R(y2)dAWhereR={(x,y)|-3鈮�x鈮�2,-2鈮�y鈮�2}
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