Calc Review 2

# Calc Review 2 - 408L Test 2 Review 1 Integration by Parts...

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408L Test 2 Review 1 Integration by Parts Z udv = uv - Z vdu Z b a udv = uv ± ± b a - Z b a vdu 2 Powers of Trig Functions Stratagy for Evaluating R sin m x cos n xdx (a) If n is odd, then save one power of cosine and use the substitution cos 2 x = 1 - sin 2 x on the other cosines. Then use the substitution u = sin x . (b) If m is odd, then save one power of sine and use the substitution sin 2 x = 1 - cos 2 x on the other sines. Then use the substitution u = cos x . (c) If both m and n are even, then use the 1/2 angle formulas: sin 2 x = 1 2 (1 - cos 2 x ) cos 2 x = 1 2 (1 + cos 2 x ) sin x cos x = 1 2 sin 2 x Stratagy for Evaluating R tan m x sec n xdx (a) If n is even, then save a sec 2 x and use the substitution tan 2 x + 1 = sec 2 x on the other secants. Then use the substitution u = tan x . (b) If m is odd, then save one sec x tan x and use the substitution tan 2 x = sec 2 x - 1 on the other tangents. Then use the substitution u = sec x . Z

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## This note was uploaded on 09/13/2011 for the course M 427K taught by Professor Fonken during the Fall '08 term at University of Texas.

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Calc Review 2 - 408L Test 2 Review 1 Integration by Parts...

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