Math 172 : Final

Wednesday Dec 11 @ 10-11:50am

Summary Points:

  The exam will cover Chapter 11 and Methods of integration.
There will be no series/sequence problems (ch 10)
There will be no application problems (ch 6, 7.7,8.1,8.2)
There will be no improper integrals.
  1. About 50% will be on Chapter 11 material (11.1-11.4). No review sheets will be posted for Ch 11 but the questions will either be homework problems or be very similar to homework problems.  You should be able to
    1. Compute arclength in parametric and polar coord.
    2. Compute areas in polar coordinates.
    3. Understand speed and slopes
    4. Convert between cartesian and polar coordinates
    Regarding the latter, you may also be asked to convert between parametric curves (x(t),y(t)) and functions y=f(x) and between polar equations and cartesian equations. There are several HW problems of this nature.
  2. About 50% will involve Methods of integration. 
    1. substitution
    2. integration by parts
    3. simple trigonometric integrals
    4. inverse trig. substitutions
    5. simple partial fraction expansions
    Problems will be similar to the review sheet and the Midterm 2 formula sheet  will be attached to the exam.
  3. A few special points
    1. For inverse trig substituion problems you must, when possible, convert your answer back to "x" without using arccos, arcsin, etc. To be clear, look at this example here.
    2. You are required to know sine and cosine of 0,Pi/6,Pi/3,Pi/4,Pi/2
  4. You should be able to do the exam in 60-75min but will have 1hr50m.

         Formula Sheet that will be attached to Final:

Formula Sheet

TECBL - Technology Enhanced Criteria Based Learning