Complete Formula Compendium

Calculus 2 · Axiom Academy

FORMULA SHEET Complete Formula Compendium The master Calculus 2 reference — every formula for integration techniques, applications, series, parametric & polar, and differential equations, in one place. Trigonometric Identities for Integration Partial Fraction Decomposition Choosing an Integration Technique Basic form? → direct integration. Composite function (chain-rule pattern)? → substitution . Product of different function types? → integration by parts . Powers of ? → trig identities . Contains , , or ? → trig substitution . Rational function (polynomial / polynomial)? → partial fractions . No elementary antiderivative? → numerical methods . Sequences & Series Fundamentals Is ? → Divergence Test (diverges). Geometric, a_n = ar^n ? → geometric-series formula. p -series, ? → converges iff . Alternating signs? → Alternating Series Test . Factorials or exponentials? → Ratio Test . A natural comparison series? → Comparison / Limit Comparison. a_n = f(n) with an easy integral? → Integral Test . Power, Taylor & Maclaurin Series Classifying a Differential Equation Order: the highest derivative present (first-order, second-order, …). Linear vs. nonlinear: linear if y and its derivatives appear only to the first power. Separable: can be written as . Homogeneous: right side equals zero, ay'' + by' + cy = 0 . Initial-value problem: includes initial conditions that pin down a particular solution.

This is the written version of the interactive lesson above. See the full Calculus 2 course.