My summary of principal subject matter for the first exam in Math 152, spring 2008

  1. Quantities computed by definite integrals
    1. Areas dx and dy.
    2. Volumes of solid objects (objects with similar slices, or solids of revolution)
    3. Work
  2. Numerical approximation of definite integrals (Trapezoid, Simpson): formulas and basic error analysis
  3. Symbolic methods for definite integrals
    1. Substitution
    2. Integration by parts
    3. Algebraic tricks (powers of trig functions, trig substitutions for square roots of quadratics, partial fractions)
  4. Improper integrals
    1. Finding limits of infinite domain integrals by taking limits of definite integrals with increasing finite domains.
    2. Finding limits of finite domain integrals where the function is unbounded by taking limits of definite integrals on increasing domains where the function is finite.
All of this is in the context of knowing the basic derivative and antiderivative formulas from Calc 1, knowing values and graphs of standard functions, and knowing how to evaluate limits, including recognizing when use of L'Hôpital's Rule is valid, and then using it.

Maintained by and last modified 2/26/2008.