20Chw6 - MATH 20C graded homework 6. (20 points) 15.1 # 26...

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Unformatted text preview: MATH 20C graded homework 6. (20 points) 15.1 # 26 (6 points): Evaluate the iterated integral R / 4 R / 2 cos (2 x + y ) dydx . Solution: Z / 4 Z / 2 cos(2 x + y ) dydx = Z / 4 sin(2 x + y ) / 2 dx = Z / 4 sin(2 x + 2 )- sin(2 x ) dx = Z / 4 sin(2 x ) cos( 2 ) + cos(2 x ) sin( 2 )- sin(2 x ) dx = Z / 4 cos(2 x )- sin(2 x ) dx = 1 2 (sin(2 x ) + cos(2 x )) / 4 = 1 2 sin( 2 ) + cos( 2 )- sin(0)- cos(0) = 0 . 15.2 # 12 (6 points): Find the double integral of f ( x,y ) = x 3 y over the region between the curves y = x 2 and y = x (1- x ) . Solution: First find the points of intersection of the two curves by solving x 2 = x (1- x ), giving x = 0 , 1 2 . ..................................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........................ . . . . . . . . . . . . ....
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This note was uploaded on 03/28/2011 for the course MATH 20C taught by Professor Helton during the Winter '08 term at UCSD.

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20Chw6 - MATH 20C graded homework 6. (20 points) 15.1 # 26...

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