ex5_fall11_2313 - Name: MAC 2313 Exam 5 Version A...

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Name: MAC 2313 Exam 5 Version A 10/31/2011 SHOW ALL YOUR WORK. Answers without procedure will be graded zero. [5] 1.Set up the integral to find the volume of the solid bounded by the paraboloid z = 2 - x 2 - y 2 and the planes x = - 1 , x = 1, y = - 1, y = 1 and z = 0. [5] 2. Set up the integral to find the volume under a surface z = f ( x,y ) and above the triangle with vertices (0 , 0) , (0 , 1) and (1 , 0). [5] 3. Sketch the region of integration and evaluate (all the way please) the integral Z 1 0 Z 1 y cos( x 2 ) dxdy
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Z 2 0 Z e x e - x f ( x,y ) dydx [6] 5. a) Sketch the polar rectangle R = { ( r,θ ) | π/ 6 θ π/ 3 , 2 r 3 } b) Describe the polar rectangle sketched below, that is, give, α,β,a and b , such that the rectangle is described as: R = { ( r,θ ) | α θ β,a r b } c) Describe the general polar region sketched below, that is, give, α,β,u 1 and u 2 , such that the region is
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ex5_fall11_2313 - Name: MAC 2313 Exam 5 Version A...

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