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Chapter 13: Q. 12 (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�0蟺鈭�x蟺siny2dydx

Short Answer

Expert verified

鈭�0蟺鈭�x蟺siny2dydx=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 above diagram, reversing the order of integration.

鈭�0蟺鈭�x蟺siny2dydx鈬�鈭�0蟺鈭�0ysiny2dydx

03

Evaluate the integral

I=鈭�0蟺鈭�0ysiny2dydxI=鈭�0蟺siny2dy鈭�0ydxI=鈭�0蟺ysiny2dyI=12-cosy20蟺I=121+1I=1

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