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Chapter 13: Q. 14 (page 1082)

Reversing the order of integration: Sketch the region determined by the limits of the given iterated integrals, and then evaluate the integrals by reversing the order of integration.

鈭�016鈭�x4211+y5dydx

Short Answer

Expert verified

鈭�0y4鈭�0211+y5dydx=15ln33

Step by step solution

01

Draw the region

The region determined by the limits of the given iterated integral is shown below,

02

Reversing the order of integration   

鈭�016鈭�x4211+y5dydx鈬�鈭�0y4鈭�0211+y5dydx

03

Evaluate the integral

I=鈭�0y4dx鈭�0211+y5dyI=鈭�02y41+y5dy

Substitute,

1+y5=t5y4dy=dtdy=15y4dtWheny=0,t=1+0=1Wheny=2,t=1+25=33

Therefore,

localid="1664260164331" I=15鈭�1331tdtI=15lnt133I=15ln33

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Most popular questions from this chapter

What is the difference between a triple integral and an iterated triple integral?

Let f(x, y, z) and g(x, y, z) be integrable functions on the rectangular solid R=x,y,z|a1猢�x猢�a2,b1猢�y猢�b2,c1猢�z猢�c2. . Use the definition of the triple integral to prove that :

鈭�Rf(x,y,z)+g(x,y,z)dV=鈭�Rf(x,y,z)dV+鈭�Rg(x,y,z)dV.

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

鈭�鈭�Rx3ex2ydA,whereR={(x,y)|0鈮�x鈮�4and鈭�1鈮�y鈮�1}

Discuss the similarities and differences between the definition of the definite integral found in Chapter 4 and the definition of the double integral found in this section.

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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