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Calculus II (Integration & Series)

Free Calculus II (Integration & Series) study guide: 9 units with summaries, key ideas, flashcards and 246 practice questions with step-by-step solutions.

Lines up with: AP Calculus BC Units 6-10.

Units

1. UNIT 01

   Review: FTC & substitution

   Calculus II builds on two ideas from Calculus I: the Fundamental Theorem and u-substitution. Get these automatic before new techniques.
2. UNIT 02

   Integration by parts

   Integration by parts reverses the product rule. Use it when the integrand is a product of two different kinds of functions.
3. UNIT 03

   Trig integrals & trig substitution

   Trig integrals use identities to reduce powers. Trig substitution uses right-triangle relationships to remove square roots.
4. UNIT 04

   Partial fractions & improper integrals

   Partial fractions split rational functions into simpler pieces you can integrate. Improper integrals handle infinite limits or infinite integrands.
5. UNIT 05

   Applications: area, volume, arc length

   Integrals measure more than area: volume, arc length, surface area and physical work are all accumulations.
6. UNIT 06

   Differential equations: Euler & logistic

   Euler's method approximates solutions step by step. The logistic model describes growth that levels off at a carrying capacity.
7. UNIT 07

   Parametric, polar & vector-valued functions

   Parametric, polar and vector-valued functions describe curves and motion that aren't simple y = f(x) graphs.
8. UNIT 08

   Sequences & convergence tests

   An infinite series adds infinitely many terms. Convergence tests tell you whether the sum is a finite number.
9. UNIT 09

   Power series & Taylor polynomials

   Power series turn functions into infinite polynomials. Taylor polynomials approximate functions near a point, with a bound on the error.