posted May 14, 2019, 4:20 AM by Matthew Grenfell
[
updated May 14, 2019, 5:15 AM
]
 Use integration by parts to evaluate integrals
 Evaluate trigonometric integrals (e.g., integrate sin^3(x),
sec^2(x)tan^2(x), and so on)
 Evaluate integrals by making trig substitutions
 Evaluate integrals using partial fractions
 Determine the convergence/divergence of improper integrals
and evaluate if convergent
 Use various tests to determine the convergence/divergence of
series, including the integral test, comparison tests, and ratio test
 Determine the convergence/divergence of a geometric series or
alternating series
 Determine a power series representation of a given function
 Determine the radius of convergence and interval of
convergence for a power series
 Determine a Maclaurin or Taylor series representation of a
function
 Determine a Taylor polynomial of a certain degree for a given
function
 Determine the solution of a separable differential equation
 Graph curves defined by parametric equations
 Determine the derivative at a point on a parametric curve
 Describe and work with points and curves in polar coordinates
 Determine areas of common regions using polar coordinates
 More integration by parts
 Approximate integration techniques (Midpoint Rule, Trapezoidal
Rule, Simpson's Rule)
 Sequences
 More power series/Taylor series (preferably deriving a Taylor
series from scratch)
 Approximating error of an integration technique or Taylor
polynomial
 Work (draining a tank, for example)
 More on parametric curves and calculus with parametric
equations

