MAT 228 Midterm: F05mt2
31 Jan 2019
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Your university id number: no calculators are allowed on this exam, please show all your work. You may use backs of pages if necessary. You may not receive full credit for a correct answer if there is no work shown. 100: (18 pts) suppose the temperature at point (x, y, z) is given by. T (x, y, z) = 3x + y2 + z3. F (x, y, z) = 2x3z 3x2y = 6. 2: (18 pts) evaluate the following iterated integrals. You can do part (b) without doing any integrating! (a) z 2. 2 sin d d d . (c) z 1. 0 x dy dx: (20 pts) (a) express the integral z 2. 2 x sin(x + y) dy dx as an equivalent integral with the order of integration reversed. Do not evaluate the integral. (to start, carefully sketch the region. ) (b) rewrite the integral z 1. 2 the integral. (xy) dy dx using polar coordinates.
