MATH 152 Midterm: MATH 152 TAMU 2009a Exam 2a Solutions
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Solutions-form a: d: the length of the curve y = x3 from x = 0 to x = 4 is l = z 4 dx. 4 u-substitution, with u = 1 + x, we obtain therefore dy dx x dx. This integral xe 3x dx = lim improper at , thus xe 3x dx. Using integra- tion by parts with u = x and dv = e 3x dx: 1 xe 3x dx = lim be 0 by l"hospital"s rule. t (cid:18) 1. 1 x2 + 1 x2 + x dx, we must rst nd the partial fraction decomposition of. Since the power in the denominator is not higher than the numerator, we must use long division. Do- x2 + 1 x2 + x x2 + 1 x2 + x. = 1 + x + 1 x2 + x. A x x + 1 ing this, we nd.
