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Chapter 13: Q. 15 (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�04鈭�y4eyxdxdy

Short Answer

Expert verified

鈭�04鈭�y4eyxdxdy=8(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 

鈭�04鈭�y4eyxdxdy鈬�鈭�04鈭�0xeyxdxdy

03

Evaluate the integral

I=鈭�04鈭�0xeyxdydxI=鈭�04eyx1/x0xdxI=鈭�04xe-1dxI=(e-1)x2204I=8(e-1)

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Most popular questions from this chapter

Explain why it would be difficult to evaluate the double integrals in Exercises 18 and 19 as iterated integrals.

鈭�鈭�RexydAwhereR=x,yI1鈮�x鈮�2and1鈮�y鈮�3

Explain how to construct a Riemann sum for a function of two variables over a rectangular region.

Expressthesum3e4+3e9+3e16+4e4+4e9+4e16usingdouble-summationnotation.

Find the volume between the graph of the given function and the xy-plane over the specified rectangle in the xy-plane

f(x,y)=-2x2y3WhereR={(x,y)|-2鈮�x鈮�3,-1鈮�y鈮�5}

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�Rxy3dAWhereR={(x,y)|-2鈮�x鈮�2,-1鈮�y鈮�1}
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