chap7sec2

chap7sec2 - = NOTE sin cos cos sin axdx ax c axdx ax c a a...

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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 m n x x dx z   (A)  If n is odd , save  cos x  and use the substitutions u x x x = = - sin cos sin 2 2 1 Example:    4 3 sin cos x xdx (B)  If m is odd , save  sin x  and use the substitutions: sin cos cos 2 2 1 x x u x = - = Example:  3 sin xdx C)  Both m and n are even , use half-angle identities: 2 2 1 1 2 2 2 2 1 1 2 2 1 2 sin (1 cos 2 ) sin (1 cos 2 ) cos (1 cos 2 ) cos (1 cos 2 ) sin cos sin 2 x x ax ax x x ax ax x x x = - = - = + = +
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Unformatted text preview: = NOTE: sin cos cos sin axdx ax c axdx ax c a a =- + = + z z 1 1 Example: 2 2 2 sin cos x xdx π ∫ II. Strategy for Evaluating tan sec m n x xdx z (A) If n is even save a 2 sec x and use these substitutions. 2 2 sec 1 tan tan x x u x = + = Example: 4 2 4 tan sec x xdx π ∫ (B) If m is odd save sec tan x x and use these substitutions. 2 2 tan sec 1 sec x x u x = - = Example: 5 3 tan sec x x dx ∫ Also: sec ln sec tan tan ln sec xdx x x C xdx x C = + + = + z z sec 2 x...
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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 - = NOTE sin cos cos sin axdx ax c axdx ax c a a...

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