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Chapter 13: Q 5. (page 1014)

Which of the iterated integrals in Exercises below could correctly

be used to evaluate the double integral:

鈭�14鈭�26f(x,y)dydx

Short Answer

Expert verified

The iterated integral will give correct value of 鈭�Rf(x,y)dA

Step by step solution

01

Given Information

Rectangular region is bounded by linesx=1,x=4,y=2andy=6

02

Definition of integral region

Consider an iterated integral

鈭�14鈭�26f(x,y)dydx

The region is rectangular with is sides parallel to xyplane.

It can be of either type.

For type I , the integration is first done with respect to yand then x.

The inner integral to be solved wrty.

03

Simplification

In 鈭�14鈭�26f(x,y)dydx, inner integral is solved wrt yand integral is solved wrt x

Hence, he iterated integral will give correct value of 鈭�Rf(x,y)dA

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Most popular questions from this chapter

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�Rx2ydAWhereR={(x,y)|-1鈮�x鈮�0,0鈮�y鈮�2}

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

鈭�-33鈭�-9-x29-x2鈭�-33f(x,y,z)dzdydx

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鈭�01鈥�鈭�03鈥�鈭�0sin鈭�1鈦�x鈥�(x+y)dzdydx

Evaluate the triple integrals over the specified rectangular solid region.

鈭�R鈥�(x+2y+3z)dV, whereR={(x,y,z)鈭�0鈮�x鈮�4,1鈮�y鈮�5,and2鈮�z鈮�7}

LetR=x,y,z|a1猢�x猢�a2,b1猢�y猢�b2,c1猢�z猢�c2.Provethat:鈭�RdV=a2-a1b2-b1c2-c1.WhatistherelationshipbetweenRandtheproducta2-a1b2-b1c2-c1.
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