MATH 152 Midterm: MATH 152 TAMU 2009a Exam 2b Solutions
Document Summary
Math 152 spring 2009 exam ii: a: x = sin t, y = cos t, thus. 2 cos tqcos2 t + sin2 t dt. 2 cos t dt = 3 : d: is. 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: 3e3t(cid:19) was found to t be 0 by l"hospital"s rule: a: x = e8y, thus dx dy. Sa = z 1: d: to nd z 2. 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. Solving for a and b, we nd x2 + 1 x2 + x dx = = 1 + x + 1 x2 + x. 1 x x + 1(cid:19) dx ing this, we nd.
