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chap7sec2 - 7.2 Trigonometric Integrals Used to integrate...

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7.2 Trigonometric Integrals Used to integrate certain combinations of trigonometric functions - especially when ordinary substitution will not work. I. Strategy for evaluating integrals of the form sin cos mn xx z d x (A) If n is odd , save cos x and use the substitutions ux x == sin cos sin 22 1 x Example: 43 sin cos d x x (B) If m is odd , save sin x and use the substitutions: sin cos cos 1 u =− = Example: 3 sin xdx C) Both m and n are even , use half-angle identities: 11 1 2 sin (1 cos 2 ) sin cos 2 ) cos cos 2 ) cos cos 2 ) sin cos sin 2 xxa x x x =+ = a x a x NOTE: sin cos cos sin axdx ax c ax c aa + = + z z Example:
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This note was uploaded on 01/20/2012 for the course MATH 2057 taught by Professor Estrada during the Fall '08 term at LSU.

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chap7sec2 - 7.2 Trigonometric Integrals Used to integrate...

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