Math 172 : Midterm 2

Tuesday, Oct 17: 6:10-8:00pm


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.

Inverse Hyperbolic functions (section 7.4) will not be on the exam. However,
you will still need to use standard substitutions (5.7) and possibly
Integration by parts (7.1).

Below is a formula sheet that will be attached to the exam including relevant trigonometric identities.

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 in the text or here).
2) About  15% will involve Improper integral(s)                       (section 7.7)
  • 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 7.8)
  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. integrals involving arcsec(u), arccsc(u), arccot(u) in sec 5.8
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.



Formula Sheet that will be attached to Midterm

Click on the image to view the PDF.

M2 formulae

TETT - Technology Enhanced Traditional Teaching Updated on: 07/24/2015.