APPM 1360 Midterm: appm1360fall2015exam1_sol
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Fall 2015: the following parts are not related: Z /4 x sec2(x) dx = x tan(x)(cid:12)(cid:12)(cid:12)(cid:12) and z /4. 0 (b)(10 pts) using partial fractions, we have x2 x + 2 (x 1)(x2 + 1) = x2 x + 2 = a(x2 + 1) + (bx + c)(x 1) a = 1, b = 0, c = 1 x2 x + 2 (x 1)(x2 + 1) dx = z. 1 x2 + 1 dx = ln|x 1| tan 1(x) + c (c)(5 pts) using integration by parts with u = f (x) du = f (x) and dv = dx v = x, we have. Determine if the integral converges or diverges, justify your answer: (c)(6 pts) z . 1 sin4(x) + e x x2 dx (d)(6 pts) z 1. You may or may not be interested to know that 1 < e < 3. ) Solution: (a)(6 pts) we rst write the improper integral as a limit.
