Calculus II Notes 16.2 - Calculus II- Stewart Dr. Berg...

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Unformatted text preview: Calculus II- Stewart Dr. Berg Spring 2010 Page 1 16.2 16.2 Iterated Integrals If we integrate a function f ( x , y ) with respect to y (treating x as a constant), we get a function of x : A ( x ) = f ( x , y ) c d dy . If we integrate A ( x ) = f ( x , y ) c d dy with respect to x , we get an iterated integral : A ( x ) a b dx = f ( x , y ) c d dy ( ) a b dx . Is f ( x , y ) c d dy ( ) a b dx = f ( x , y ) a b dx ( ) c d dy ? Example A Find the integral of f ( x , y ) = x 2 xy over the rectangle R = [0,2] [0,2] in both orders. Solution : x 2 xy ( ) 2 2 dx dy = x 3 3 x 2 y 2 2 2 dy = 2 3 3 2 2 y 2 2 2 dy = 8 3 2 y 2 dy = 8 3 y y 2 2 = 16 3 4 = 4 3 . Also x 2 xy ( ) 2 2 dy dx = x 2 y xy 2 2 2 2 dx = 2 x 2 2 x ( ) 2 dx = 2 x 3 3...
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This note was uploaded on 04/04/2011 for the course MATH 408 L taught by Professor Zheng during the Spring '10 term at University of Texas at Austin.

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Calculus II Notes 16.2 - Calculus II- Stewart Dr. Berg...

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