MATH 132 Study Guide - Midterm Guide: Trapezoidal Rule, Partial Fraction Decomposition
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3/26/09: [12%] for the trapezoidal rule with n = 4, we have x = 2(cid:19) + 2f (1) + 2f (cid:18) 3. Or you could set this up using a table: i. P wif (xi: [12%] z (cid:0)x x + 5e 5x(cid:1) dx = z (cid:16)x3/2 + 5e 5x(cid:17) dx = 5 x5/2 e 5x + c: [12%] begin by using parts: u = arctan x dv = dx du = In the last integral explicitly (or implicitly) substitute: 1 + x2 dx = u = 1 + x2 du = 2x dx du = x dx. 2 z 1 ln(cid:0)|u|(cid:1) + c ln(cid:0)|1 + x2|(cid:1) + c ln(cid:12)(cid:12)1 + x2(cid:12)(cid:12) + c. 2 (the absolute value may be removed inside ln because 1 + x2 > 0. ) 1: [12%] factor x2 5x + 4 = (x 1) (x 4).
