MATH 129 FINAL EXAM REVIEW PACKET (Revised Fall 2010) The following questions can be used as a review for Math 129. These questions are not actual samples of questions that will appear on the final exam, but they will provide additional practice for the material that will be covered on the final exam. When solving these problems keep the following in mind: Full credit for correct answers will only be awarded if all work is shown. Exact values must be given unless an approximation is required. Credit will not be given for an approximation when an exact value can be found by techniques covered in the course. The answers, along with comments, are posted as a separate file on http://math.arizona.edu/~calc. 1. Suppose the rate at which people get a particular disease (measured in people per month) can be modeled by( )10sin303r ttππ=+. Find the total number of people who will get the disease during the first three months (03t≤≤). 2. If 31( )7f u du=∫, find the value of 21(52 )fx dx−∫. 3. Evaluate 1tdtt+∫4. Use the method of integration by parts: a) Evaluate ()22ln1zdzz+∫b) Evaluate 2arcsin()xxdx∫. c) Letgbe twice differentiable with(0)6g=, (1)5g=, and (1)2g′=. Find 10( )x gx dx′′⋅∫. 5. Evaluate the following integrals (you can use the table of integrals): a)2cos (32)dθθ+∫b) 2249dtt−∫c) 2815dyyy++∫6. Use the method of partial fractions to evaluate 33351yydyyy+−+∫.
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