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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.

016x4211+y5dydx

Short Answer

Expert verified

0y40211+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   

016x4211+y5dydx0y40211+y5dydx

03

Evaluate the integral

I=0y4dx0211+y5dyI=02y41+y5dy

Substitute,

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

Therefore,

localid="1664260164331" I=151331tdtI=15lnt133I=15ln33

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