2-9 - February 9, 2005 Today 7.5 Strategy for Integration 1...

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Unformatted text preview: February 9, 2005 Today 7.5 Strategy for Integration 1 Table of indefinite integrals Z x n dx = x n +1 n + 1 + C ( n 6 =- 1) Z 1 x dx = ln | x | + C Z e x dx = e x + C Z sin xdx =- cos x + C Z cos xdx = sin x + C Z sec 2 xdx = tan x + C Z 1 sin 2 x dx =- cos x sin x + C Z sec xdx = 1 2 ln 1 + sin x 1- sin x + C Z 1 a 2 + x 2 dx = 1 a arctan x a + C Z 1 q a 2- x 2 dx = arcsin x a + C Steps to evaluate an integral 1. Simplify the integrand 2. Does substitution work? 3. Does integration by parts work? 4. Classify the integrand: Trigonometric function Rational function Contains radicals 5. Take a second look: either substitution or integration by parts must work (maybe af- ter manipulation of the integrand). Integration strategy You might want to follow these steps when evaluating an integral. Be prepare to abandon an attempt and proceed with another. Do not get discouraged. It takes lots of practice to master all the techniques....
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2-9 - February 9, 2005 Today 7.5 Strategy for Integration 1...

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