MATH 125 Midterm: MATH 125 UW 125 Fall 11 Sol2

• School: UW
• Department: Mathematics
• Course: MATH 125
• Professor: All

Document Summary

Math 125, sections e and f, fall 2011, solutions to midterm ii: evaluate the following inde nite integrals. (a) u-sub u = sin(3t) du = 3 cos(3t)dt. 3 tan 1(sin(3t)) + c (b) partial fractions, case iii. 2x2 + 3x + 4 (x 1)(x2 + 9) 30 tan 1(cid:16) x: evaluate the following integrals. (a) inverse trig substitution x = 2 sec dx = 2 sec tan . 8 sec3 (b) integration is by parts. 1 ln x x3 dx = lim t z t. 1 t ln x x3 dx = lim t. 3. (a) use simpson"s rule with n = 6 to approximate the integral ex. [f (0) + 4f (1/6) + 2f (2/6) + 4f (3/6) + 2f (4/6) + 4f (5/6) + f (1)] 0. 6201149 (b) evaluate the same integral exactly and nd the percentage error in your simpson"s rule approx- imation. Percentage error= error actual value 100 percent. ex.