MATH 234 Final: 234fall14FinalSol
15 Feb 2019
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Instructions: read each problem carefully, write legibly, show all your work on these sheets, make sure that your nal answer is clearly indicated. If two answers are presented then the average of the points for each answer will be given: this exam has 10 pages, and 9 problems. Before starting the exam, please check that your copy contains all of them and obtain a new copy of the exam immediately if it does not: you may not use books, notes or calculators. Question 1 (10 points). (1) sketch the region d in the double integral. 0 z 2 2x x2 f (x, y) dy dx. (2) rewrite the double integral as an iterated integral with the order interchanged. Z 2 x2 f (x, y) dy dx = z 4. X2+y2 as an iterated integral in spherical coordinates. 5 cos sin cos sin3 d d d . Evaluate the following integral by using the given change of variables.
