M408C - Brian's Draft Cheat Sheet

M408C - Brian's Draft Cheat Sheet - -split num erator use...

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Area BTW Curves -Find Intercepts -Integrate Between Intercepts + Want Positive Area Hyperbolic Trig + c + c Critical Points -CP = First Derivative Test - Separate interval according to intercepts - Find the sign of on each interval - - Integration by Parts Trig Substitution Product of Trig Functions - M odd o Save 1 and write the rest as sin x; U = sin x - N Odd o Save 1 sin x and write the rest as cos x; U = cos x - Otherwise: Everything as sin x; Use recursion formulas - M Odd, N ≥ 1 o Save tan x sec x ; write rest as sec x ; u = sec x - N Even, M ≥ 2 o Save - Otherwise: Everything in sec x; use recursion formula - N Odd o Save sin x, write the rest as cos x: u = cos x - Otherwise: Write everything in terms of cos x
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Unformatted text preview: -split num erator; use recursion-N Odd o Save cos x, write the rest as sin x: u = sin x-Otherwise: Write everything in terms of sin x-split num erator; use recursion Integrating Rational Functions 1. If deg p (x) = deg q (x) use long division 2. Partial Factions a. Individual Linear Factors – (x – a) b. Repeated ILF – c. Individual Quad Factors – ( d. Repeated IQF – a. ILF = b. RILF = + c. IQF = d. RIQF = + -Factor Q (x)-Common Denominator-Solve for Coefficient-Integrating IQF o Complete Square in IQF o U-Sub to make IQF look like o Separate the num erator o Integrate to get sums of logs and inverse trig =...
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