Quiz 1

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Department
Mathematics & Engineering Courses
Course
MTHE 225
Professor
Gregory G Smith
Semester
Fall

Description
Quiz 1 Solutions (i) Find the following inde▯nite integrals (a) Z lnxdx: Use integration by parts. Set u = lnx, dv = dx, so v = x. Then Z Z 1 lnxdx = xlnx ▯ x dx Z x = xlnx ▯ dx = xlnx ▯ x + C (b) Z 1 dx: x + 3x + 2 Use partial fractions. Find A, B such that 1 A B x + 3x + 2 = x + 1+ x + 2 We must have 1 = A(x+2)+B(x+1) = (A+B)x+2A+B, so A = 1;B = ▯1. Thus Z Z Z 1 dx = 1 dx ▯ 1 dx x + 3x + 2 x + 1 x + 2
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