MATH 31B Study Guide - Midterm Guide: Direct Comparison Test, Improper Integral
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If the question is in several parts, carefully label the answer to each part. Do all of your work on the examination paper; scratch paper is not permitted. If you continue a problem on the back of the page, please write continued on back . Problem 1: (a) evaluate the inde nite integral: (b) evaluate the inde nite integral: (cid:90) (cid:90) tan2 x sec6 x dx arctan x (1 + x2)3/2 dx. Problem 2: (a) evaluate the improper integral: (cid:90) . 1 x + 1 x4 + x2 dx. (b) use the comparison test to determine if the improper integral converges: Problem 3: (a) find m4 and s4 for (cid:90) 4. 2 ex dx (you do not need to simplify your expressions). (b) does m4 give an overestimate or underestimate of the integral? (c) compute the error bound for s4.
