MATH 132 Midterm: MATH 132 UMass Amherst 132s05xf
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Problem 1 evaluate each integral. (a) (6 points) xe2xdx. 2 xe2x 1 xe2x 1. 2 e2x c. (b) (9 points) e x cos 2xdx. Let u e x and dv cos 2x. Then, du e xdx and v 1. Now, let u e x and dv sin 2x. Using integration by parts again, we have e x sin 2x 1. 2 1 e x cos 2x 1. 2 e x sin 2x 1 e x sin 2x 1. 4 e x cos 2xdx 1 e x cos 2x, which implies that.
