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1. Let A;B  Rn and assume A and B have area. Prove A [ B has area, prove AnB has area. 2. Reverse the order of integration Z 4 1 Z p y p y􀀀1 F(x; y)dx ! dy 3. Calculate Z 1 0 Z 1 x e􀀀y2 dy dx 5.10. Use double polar coordinates dened by the equations x1 = r cos ; x2 = r sin ; x3 =  cos ; x4 =  sin  to show that the volume of the unit ball B4  R4 is 1 22. 5.11. Use the transformation dened by u = 2x x2 + y2 ; v = 2y x2 + y2 to evaluate Z Z R dxdy (x2 + y2)2 1

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