Name : ______________________
Exam 2 - Chapter 9, 100 points
Math 122 - Calculus & Analytic Geometry II

  1. Find the average water level on the Sangamon River at Illinois Rt 48 in Decatur, IL at for the month of February 1999. Use the URL and request the "stage" data for 30 days in a tab delimited file. Record the times at midnight on 2/1/99 through midnight on 3/1/99 so that you have a full 28 days of information (but 29 endpoints). Also record the water stage at noon for each day in February. You may want to get some of the early information recorded now because there are only 30 days worth of information and you need 28 of them. Attach a table of the values used. (10 points)
    1. Using the 29 values recorded at midnight, approximate the average water stage using the left-hand endpoints, right-hand endpoints, trapezoidal method, and Simpson's method
    2. Using the 28 values recorded at noon, approximate the average water stage using the midpoints.
  2. Work the "Railroad Design" activity on pages 576 - 578. Your results should be presented in packet form as if you were going to present this information as an engineer's report. Have a well designed executive summary page with a breakdown of costs for both techniques. This should start off with a description of the problem. Follow that with a summary of the results of each technique including a brief explanation of the process, an itemized cost list including quantity, per unit cost, and extended cost, and a total cost. Give a recommendation as to which technique should be used and the cost savings. The tables and work can be attached as supplemental information. (10 points)
  3. Find the following Laplace Transforms (look at problems 9.8.56-57). Note that the Laplace Transform is a function of s only, there is no x in the transform. The restrictions on s that are given in the book are necessary so that the improper integral converges, be sure to state proper restrictions. (10 points)
  4. Work supplemental problem 36 involving the Gamma function. (10 points)
  5. Use a table of integrals to find the integral. In each case, copy the integral number and formula and the values of any variables (ex: a or u) (10 points)
    1. Problem 9.6.10
    2. Problem 9.6.20
    3. Problem 9.6.24
    4. Problem 9.6.30
    5. Problem 9.6.38
  6. Use a computer algebra system (Derive, Maple, Mathematica, TI-92) to find the following integrals. (10 points)
    1. Problem 9.6.42
    2. Problem 9.6.50
    3. Problem 9.6.56
    4. Problem 9.6.62
    5. Problem 9.6.70
  7. Work any ten (10) of the following problems by hand. Show all work. You may use the reduction formulas where necessary, but otherwise do not use the table of integrals. You may use a CAS to check your answer, but show work. (40 points)
    1. Problem 9.2.8
    2. Problem 9.2.38
    3. Problem 9.3.8
    4. Problem 9.3.34
    5. Problem 9.4.12
    6. Problem 9.4.18
    7. Problem 9.4.40
    8. Problem 9.5.20
    9. Problem 9.5.24
    10. Problem 9.8.8
    11. Problem 9.8.27
    12. Problem 9.8.42

The entire test is take home. You may the first four problems in groups of up to three and turn in one paper per group, but each student's exam should contain the answers to the rest of the problems. Be sure you double check and understand the work of those in your group, it's your grade, too.