MATH 132 Study Guide - Final Guide: Improper Integral, Symbolic Integration, Trapezoidal Rule
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Section # university of massachusetts amherst department of mathematics and statistics. Instructions: turn o cell phones and watch alarms! Put away cell phones, ipods, etc: there are seven (7) questions, do all work in this exam booklet. Be prepared to show your umass id card. 100: (2 7% = 14%) the parts of this question are not related! (a) approximate the integral with n = 4 subintervals. Round your answer to 4 decimal places. (cid:2) 1. 1 +x 3 dx by using the trapezoidal rule (b) starting with the maclaurin series for ex, nd a power series expansion of x2 e x. 2: (2 6 = 12%) use techniques of symbolic integration to evaluate: (cid:2) (a) arcsin x dx(hint: try integration by parts. ) (cid:2) (b) Continuation of # 4. (c) (7%) set up and evaluate a de nite integral in order to nd the area of the region enclosed by the polar curve r = 3 cos .
