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Unformatted text preview: 27 . So the center of mass is at ( M y /m,M x /m ) = (27 / 20 , 3 / 2). 3. By drawing a picture, one sees that the region in question is the triangle with vertices (0 , 0), (0 , 1) and (1 , 1). So if we interchange the order of integration, the integral becomes Z 1 Z y (1y 2 ) 1 3 dxdy = Z 1 y (1y 2 ) 1 3 dy = 3 8 . 4. Converting to spherical coordinates, the integral becomes: Z π 2 Z π 2 Z 2 1 eρ 2 ρ ρ 2 sin φdρdφdθ = Z π 2 Z π 2 ±1 2 eρ 2 ² 2 1 sin φdφdθ = π 4 ( e1e4 ) ....
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This note was uploaded on 10/20/2011 for the course MAC 2313 taught by Professor Keeran during the Fall '08 term at University of Florida.
 Fall '08
 Keeran
 Calculus, Geometry

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