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Chapter 13: Q. 32 (page 1004)

Use definition to evaluate the double integral

鈭鈭Rx2y3dAWhereR={(x,y)|1鈮x鈮3,0鈮y鈮2}

Short Answer

Expert verified

The value of the integral is 126

Step by step solution

01

Given information

We are given a double integral

鈭鈭Rx2y3dAWhereR={(x,y)|1鈮x鈮3,0鈮y鈮2}

02

Use definition to find the value of double integral

We get,

鈭i=02鈭x2y3j=13=鈭i=02(y3+4y3+9y3)=鈭i=02(14y3)=14(1)+14(8)=126

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Most popular questions from this chapter

Evaluate the sums in Exercises 23鈥28

鈭i=1l鈭j=1m鈭k=1mij2k3

Evaluate the triple integrals over the specified rectangular solid region.

鈭R鈥ln鈦xyz2dV, whereR={(x,y,z)鈭1鈮x鈮3,1鈮y鈮e,and1鈮z鈮2}

Evaluate the iterated integral :

鈭13鈥鈭鈭15鈥鈭03鈥xy2zdzdydx

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}

Use Definition 13.4to evaluate the double integrals in Exercises 29鈥32.

鈭Rxy3dA

whereR={(x,y)鈭-2鈮x鈮2&-1鈮y鈮1}
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