Math 172 : Midterm 2

Date: Tuesday, March 17, 6:00-7:50pm

Summary Points:  
1)       Approximately 50% the exam will be straight up integration problems
  1. Trigonometric Integrals                                            (section 7.2)
  2. Trigonometric Substitution                                        (section 7.3)
  3. Method of Partial Fractions                                        (section 7.5)        
You will have to do at least one of each of the three types of integrals above.
Below is a formula sheet that will be attached to the exam which includes relevant trigonometric identities.

You will need to use standard substitutions (5.6) but not Integration By Parts (7.1)

For trigonometric substitutions you must use the triangle method
to convert your answer back to the original variables (see Figures 1-4 of 7.3)
2) About  15% will involve Improper integral(s)                       (section 7.6)
  • Know the convergence for integrands 1/x^p on (0,1) and (1,infinity)
  • Know the comparison test (including positivity requirement)
  • Always use limit notation when evaluating convergent integrals.
3) The balance of the exam will be on integral applications
  1. Probability Theory                                                    (section 7.7)
  2. Arclength or Surface Area of Revolution                     (section 8.1)
  3. Fluid Pressure                                                          (section 8.2)
There will be a question on all 3 topics above.
4) Some noteable exclusions from the exam are:
  1. integrals involving hyperbolic functions, i.e. all of sec 7.4
  2. integration by parts sec 7.1
  3. integrals involving arcsec(u), arccsc(u), arccot(u) in sec 5.7
5) A formula sheet (below) will be attachedto the exam
6) You are expected to evaluate sine, cosine and tan of multiples of Pi/6, Pi/3, Pi/4, Pi/2
as well as evaluate inverse trig functions (arcsin, arccos, arctan) of 0, 1/2,1. Also you
need to know ln(e)=1 and ln(1)=0.
7) Exam questions are variants of homework problems. Generally speaking the HW is a very good guide to the kinds of problems on the test.  
8) You should be able to do the exam in 60-75min but will have 1hr and 50min  
9) Remember our tutoring resources - both the Math Learning Center and review sessions held by Corinne Casolara (SSC).  

      Formula Sheet that will be attached to Midterm:

Midterm 2 Formula Sheet

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