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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 9-y f ( x,y ) dxdy . 6) Using Polar Coordinates, evaluate R 2 R 2 x-x 2 p x 2 + y 2 dydx . 7) Let E denote the solid bounded by the surfaces y = 4-x 2-4 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 2-2 Z 4-y 2- 4-y 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 a-a Z a 2-y 2- a 2-y 2 Z a 2-x 2-y 2- a 2-x 2-y 2 ( x 2 z + y 2 z + z 3 ) dzdxdy . 2...
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