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Unformatted text preview: 5) Sketch the region of integration and change the order of integration for the integral R 3 R 9y f ( x,y ) dxdy . 6) Using Polar Coordinates, evaluate R 2 R 2 xx 2 p x 2 + y 2 dydx . 7) Let E denote the solid bounded by the surfaces y = 4x 24 z 2 and y = 0. Express the integral R R R E f ( x,y,z ) dV by interpreting dV as (i) dydzdx (ii) dzdydx (iii) dxdydz 1 8) Evaluate (i) the volume of the solid bounded by the surfaces y = x 2 , z = 0, z = 4, and y = 9. (ii) Z 22 Z 4y 2 4y 2 Z 2 x 2 + y 2 xz dzdxdy (iii) R R R E xyz dV where E lies between the spheres x 2 + y 2 + z 2 = 4 and x 2 + y 2 + z 2 = 16 and above the cone = 3 . (iv) Z aa Z a 2y 2 a 2y 2 Z a 2x 2y 2 a 2x 2y 2 ( x 2 z + y 2 z + z 3 ) dzdxdy . 2...
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This note was uploaded on 12/15/2011 for the course MAC 2313 taught by Professor Keeran during the Spring '08 term at University of Florida.
 Spring '08
 Keeran
 Calculus, Geometry

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