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Chapter 13: Q. 35 (page 1004)

Evaluate Each of the integrals in exercises 33-36 as an iterated integral and then compare your answer with thoise you found in exercise 29-32

鈭�鈭�Rxy3dAWhereR={(x,y)|-2鈮�x鈮�2,-1鈮�y鈮�1}

Short Answer

Expert verified

The value of integral is 0

Step by step solution

01

Given information

We are given an integral鈭�鈭�Rxy3dAWhereR={(x,y)|-2鈮�x鈮�2,-1鈮�y鈮�1}

02

Use iteration method to evaluate integral

We get,

鈭�-11鈭�-22xy3dxdy=鈭�-11[x2y32]2-2dy=鈭�-11[0]dy=0

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Most popular questions from this chapter

Describe the three-dimensional region expressed in each iterated integral in Exercises 35鈥�44.

鈭�02鈭�01-3x/2鈭�2x+(4/3)y-40f(x,y,z)dzdydx

Expressthesum25+26+27+28+45+46+47+48usingdouble-summationnotation.

Describe the three-dimensional region expressed in each iterated integral in Exercises 35鈥�44.

鈭�03鈭�03鈭�03-yf(x,y,z)dzdydx

Use the results of Exercises 59 and 60 to find the centers of masses of the lamin忙 in Exercises 61鈥�67.

In the following lamina, all angles are right angles and the density is constant:

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

鈭�鈭�RxexydA,where{R=(x,y)|0鈮�x鈮�1and0鈮�y鈮�ln5}
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