Summary of Integration Methods
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Summary of Integration Techniques I FTC part II: Z b a F 0 (x ) dx = F (b) - F (a) I Antiderivatives Table I Substitution: Z f (u(x )) · u 0 (x ) dx = Z f (u) du I Integration by Parts: Z u dv = u · v - Z v du, or Z f (x ) · g 0 (x ) dx = f (x ) · g (x ) - Z f 0 (x ) · g (x ) dx I Trigonometric Integrals: use a trigonometric substitution, a trigonometric identity or both. I Partial Fractions for Z polynomial polynomial dx ❀ factor denominator, decompose into partial fractions, integrate I Approximate Integration + any combination thereof.
Transcript of Summary of Integration Methods
Summary of Integration Techniques
I FTC part II:
∫ b
aF ′(x) dx = F (b) − F (a)
I Antiderivatives Table
I Substitution:
∫f (u(x)) · u′(x) dx =
∫f (u) du
I Integration by Parts:
∫u dv = u · v −
∫v du, or∫
f (x) · g ′(x) dx = f (x) · g(x) −∫
f ′(x) · g(x) dx
I Trigonometric Integrals: use a trigonometric substitution, atrigonometric identity or both.
I Partial Fractions for
∫polynomial
polynomialdx ; factor denominator,
decompose into partial fractions, integrate
I Approximate Integration
+ any combination thereof.
