MATH128 Study Guide - Quiz Guide: Partial Fraction Decomposition
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0 [tan3 sec2 tan (sec2 1)] d = /4. 0 (tan3 tan ) sec2 d + /4. Total is 50: solve the following integrals, 4/ Let u = tan ; du = sec2 d , and u(0) = 0, u( /4) = 1 so the first integral becomes. 0 (u3 u) du = (1/4) u4 (1/2)u2 |1. 0 [(tan3 tan ) sec2 + tan ] d . 0 tan5 d = (1/2) ln 2 (1/4). 0 = ln | 2| ln|1| = (1/2) ln 2. d. Let z = x , dz = 2x dx. ; let x 1 = sin t and d(x 1) = dx = cos t dt. 211 t cos t cos cos cos sin tdt dx dx dx dx dx x x. So 2a = 1 a = ; while 2b c = 4. 5 and b + c = 1. 5 3b = 6 or b = 2 and c = . xbx.
