MATH 181 Study Guide - Final Guide: 4Dx, Midpoint Method, Trapezoidal Rule
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2 du = x dx and we get: X dx dx = ! ex eu. 4 arctan u + c arctan(4x) + c. Then du = 4t3 dt du = t3 dt and we get: Problem 4 solution: evaluate ! tan2 sec2 d . Then du = sec2 d and we get: tan2 sec2 d = ! u2 du. 0 x 1 x2 dx: evaluate ! The limits of integration becomes u = 1 02 = 1 and du = 2x dx . 2 u = 1 12 = 0. 2 $ 2 u3/2%1 (1)3/2% u1/2 du u1/2 du. Problem 6 solution: evaluate ! cos x. 4 + 3 sin x dx. du = cos x dx. The limits of integration become u = 4 + Solution: we evaluate the integral using the u-substitution method. Let u = 4 + 3 sin x. Then du = 3 cos x dx . 4 because the limits of integration are identical.
