My summary of principal subject matter for the
first exam in Math 152, spring 2008
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
- Quantities computed by definite integrals
- Areas dx and dy.
- Volumes of solid objects (objects with similar slices, or solids
- Numerical approximation of definite integrals (Trapezoid,
Simpson): formulas and basic error analysis
- Symbolic methods for definite integrals
- Integration by parts
- Algebraic tricks (powers of trig functions, trig substitutions for
square roots of quadratics, partial fractions)
- Improper integrals
- Finding limits of infinite domain integrals by taking limits of
definite integrals with increasing finite domains.
- 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.
firstname.lastname@example.org and last modified 2/26/2008.