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Summary of Integration Methods
This document summarizes several integration techniques including the fundamental theorem of calculus, substitution, integration by parts, trigonometric integrals, partial fractions, and approximate integration. It explains that the fundamental theorem relates antiderivatives to definite integrals, substitution allows integrals with functions of functions to be evaluated, and integration by parts and partial fractions are used to decompose integrals that cannot be directly evaluated. Trigonometric integrals may use trigonometric substitutions or identities while approximate integration provides numerical approximations.
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Summary of Integration Methods
- 1. Summary of IntegrationTechniques b FTC part II: F (x) dx = F (b) − F (a) a Antiderivatives Table Substitution: f (u(x)) · u (x) dx = f (u) du Integration by Parts: u dv = u · v − v du, or f (x) · g (x) dx = f (x) · g (x) − f (x) · g (x) dx Trigonometric Integrals: use a trigonometric substitution, a trigonometric identity or both. polynomial Partial Fractions for dx ; factor denominator, polynomial decompose into partial fractions, integrate Approximate Integration + any combination thereof.