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Chapter 13: Q. 16 (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�01鈭�x1exy2dydx

Short Answer

Expert verified

鈭�01鈭�x1exy2dydx=13(e-1)

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 

From the diagram, the order of differentiation is changed,

鈭�01鈭�x1exy2dydx鈬�鈭�01鈭�0y2exy2dydx

03

Evaluate the integral

I=鈭�01鈭�0y2exy2dxdyI=鈭�01exy21/y20y2dyI=鈭�01y2e-1dyI=(e-1)y3301I=13(e-1)

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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�03鈭�03鈭�03-yf(x,y,z)dzdydx

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localid="1649936867482" 鈭�xx2ydA

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