MATH 234 Final: Math 234 Spring 2013 Final
15 Feb 2019
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Instructions: mark your section, read each problem carefully, write legibly, show all of your work on these sheets, the exam consists of 10 problems and 11 pages. Please verify that you have all 11 pages: you may not use books, notes or calculators, you have 120 minutes to complete this exam. Page 2 of 11: (10 points) consider the iterated double integral. Y (a) sketch the region of integration. (b) evaluate the double integral by reversing order of integration. Page 3 of 11: (10 points) evaluate the triple integral. Zzzd x dv where d the solid region in the rst octant bounded by the parabolic cylinder z = x2 and the plane y + z = 1. Page 4 of 11: (10 points) use cylindrical coordinates to evaluate the volume of the solid region. D that lies below the hemi-sphere z = p4 x2 y2 and above the plane z = 1.
