Instructions

  1. Exam scores count for 30% of your grade (there will be two or three).
  2. The exam has 8 exercises for 100 points and is designed to be completed in 50 minutes.
  3. You may use a calculator with factory-shipped programs, 1 side of a 8.5 by 11 inch page written in your own handwriting, and a writing utensil, but nothing else. NO PHONES OR COMPUTERS.
  4. You should simplify expressions and leave exact values unless directed otherwise.
  5. To earn full credit, justify your solutions and always indicate your methods.
  6. This is a guide, which means the exercises are different from actual exam questions.
  7. The exam covers sections 6.1-6.4, 6.6, 7.1-7.4, 7.7 of the text plus in-class content and generalizations.

Big Ideas on Exam 2

Applications

  1. Volumes of Solids - definition of volume as an integral, applying formulas for the disc method, washer method, and cylindrical shells method.
  2. Arc Length – especially setting up the integrals, and including parametric curves.
  3. Work- definition of work as an integral of forces, applications to pumping and lifting.
  4. Income Streams – applications of future value as an integral of continuously compounded income stream  at a variable interest rate .

Techniques

  1. Integration by Substitution – identifying the “inner function” and transforming the integral
  2. Integration by Parts – including the tabular method for repeated integration by parts and the LIPET heuristic.
  3. Trig Integrals – especially those using the tangent reduction formula and products of the form .
  4. Trig Substitution –choosing the correct substitution (based on the form of the integrand),transforming the integral, simplifying with trig identities, using the reference triangle to rewrite in terms of the original variable
  5. Partial Fractions – especially when the denominator has two distinct roots.
  6. Improper Integrals – the two types and how to reason through the limiting aspect of the evaluation.
Posted on October 28, 2011 by Joe Champion » Show Details.