Trig_integrals_slides

Trig_integrals_slides - Section 8.3 Trigonometric Integrals...

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Unformatted text preview: Section 8.3: Trigonometric Integrals cos a ( x )sin b ( x ) dx ! Done by substitution: u= sin(x) or u=cos(x). how do we pick cos a ( x )sin b ( x ) dx ! Done by substitution: u= sin(x) or u=cos(x). how do we pick the right u? cos( x )sin 6 ( x ) dx ! A) u= sin(x) B) u=cos(x) I = cos( x )sin 6 ( x ) dx ! A) u= sin(x) du= cos(x)dx I = u 6 du = ! u 7 7 + c = sin 7 ( x ) 7 + c cos 4 ( x )sin 5 ( x ) dx ! A) u= sin(x) B) u=cos(x) If the power of cosine is odd , make the substitution u=sin(x) If the power of sine is odd make the substitution u=cos(x) If both the powers of sine and cosine are even , keep using the formulas for the half angles to reduce to one of the previous 2 cases cos a ( x )sin b ( x ) dx ! how do we pick the right u? cos 4 ( x )sin 5 ( x ) dx ! Odd power of sine Even power of cosine Follow the recipe for when an odd power of sine shows up… If the power of the sine is odd:- Save one power of sine- Use the identity cos 2 (x)+sin 2 (x)=1 to express the remaining powers of sin(x) in terms of cos(x)...
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This note was uploaded on 12/07/2010 for the course MATH MATH 2B taught by Professor Famiglietti,c during the Fall '09 term at UC Irvine.

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Trig_integrals_slides - Section 8.3 Trigonometric Integrals...

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