MATH 234 Midterm: Math 234 Winter 2012 Test 1
15 Feb 2019
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Instructions: read each problem carefully, write legibly, show all of your work on these sheets, the exam consists of 5 problems and 6 pages. Please verify that you have all 6 pages: you may not use books, notes or calculators, you have 50 minutes to complete this test. Page 2 of 6: (10 points) in evaluating a double integral over a region d, a sum of iterated integrals was obtained as follows. Zzd f (x, y) da = z 1. Y f (x, y) dx dy +z 3. Y f (x, y) dx dy. (a) sketch the region d. (b) express the double integral as one iterated integral with reversed order of integration. Page 3 of 6: (10 points) evaluate the triple integral. Zzze y dv where e is the solid tetrahedron bounded by the planes x + y + z = 2, y = x, y = 0, and z = 0.
