MAC 2313 Midterm: MAC2313 F09 Test 3
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Write your complete solutions on the answer sheets. Do not write on this test paper. (1) (20 points) sketch the region r in the xy-plane de ned by the inequalities x 0, y 3x, y x(x2 1). Do (c) express the integral of part (b) using polar coordinates. Do not evalu- ate. (3) (10 points) let s denote the solid in xyz-space de ned by the inequalities y 0, 0 z 4 y x2. Set up, but do not evaluate, a triple iterated integral for the volume of s. (4) (10 points) let s denote the solid region in xyz-space de ned by the in- equalities. 0 z 5 x2 y2. Set up, but do not evaluate, a triple iterated integral for the volume of s. (5) (30 points) let d denote the solid in xyz-space de ned by the inequalitites. 0 z x2 + y2, x2 + y2 1. (a) express the integral rrrd zdv using rectangular coordinates.
