MTH 162 Final: MTH 162 University of Rochester Fall 11Finalsol

• School: University of Rochester
• Department: Mathematics
• Course: MTH 162
• Professor: All

Document Summary

Part a: (20 points) (a) find the partial fraction expansion of (b) calculate the integral. Note: the rst part of this problem was designed to help you do the second part. If you did the rst part incorrectly, you will not get partial credit for correctly using the wrong partial fraction expansion to nd the integral. Solution: (a) x3 x2 6x = x(x + 2)(x 3). 1 = a(x + 2)(x 3) + b(x)(x 3) + c(x)(x + 2). Setting x = 0 gives 1 = 6a or a = 1/6, setting x = 2 gives 1 = 10b or b = 1/10, and setting x = 3 gives 1 = 15c or c = 1/15. Math 162 (calculus iia) (b) from (a) we get. 1 x3 x2 6x dx = z (cid:18) . 15 ln|x 3| + c: (20 points) evaluate the integral. [hint: you may nd the identity sin(2 ) = 2 sin cos useful. ]