Final Exam Study Guide

The exam will have 200 points worth of questions on it, and thus be roughly equivalent to an exam twice as long as an hour exam. But you'll have 3 hours to work on it.

I would like you to be able to explain, loosely, as I did in class, why Part 1 of the Fundamental Theorem of Calculus, is true. (The proof on page 392 is much more rigorous.)

  • Chapters 1-5.3 as covered in the Exam 1 Study Guide and the Exam 2 Study Guide and the Exam 3 Study Guide.
  • Chapter 5
  • 5.4: antiderivatives and the total change theorem
  • 5.5: integration by substitution, both with and without limits (i.e., both indefinite and definite integrals). Be sure to become skillful at guessing which substitution to do!
  • 5.6: skip.
  • Chapter 6
  • 6.1: area between curves, horizontal or vertical strips
  • 6.2: volumes by slicing, solids of revolution (horizontal or vertical), disks and washers, and the general case (where the cross sections are simply described.
  • 6.3: skip.
  • 6.4: physics: work done under a variable force as an integral (i.e., as an area)
  • 6.5: average values of functions on intervals (just the first part of the section)
  • Chapter 8
  • 8.3: physics: water pressure, total force as an integral, and some of (depending on the extent of today's lecture): moments (weighted averages), centers of mass (centroids), and Pappus' theorem.