Guidelines For Trig Integrals

Guidelines For Trig Integrals - Case 1: Power on the secant...

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Guidelines For Trig Integrals When handling trig integrals, how you approach the problem will depend on which trig functions are involved and the powers on the functions. Powers and products of sine and cosine Case 1: Sine is raised to an odd power Save one sine factor for a u-substitution and convert the rest of the factors to cosine. Expand and then integrate. Case 2: Cosine is raised to an odd power Save one cosine factor for a u-substitution and convert the rest of the factors to sine. Expand and then integrate. Case 3: Sine and cosine are raised to an even power Using the power reducing formulas ( 2 ) 2 cos( 1 ) ( sin 2 x x - = , 2 ) 2 cos( 1 ) ( cos 2 x x + = ), convert to an integral cosines raised to the 1 st power and use u-substitution to integrate. Repeated use of the power reducing formula maybe needed. Powers and products of tangent and secant
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Unformatted text preview: Case 1: Power on the secant is even Save a secant-squared factor and convert the rest to tangents. Expand and then integrate. Case 2: Power on tangent is odd Save a secant-tangent factor and convert the rest of the tangent terms to secants. Expand and then integrate. Case 3: Power on tangent is even and there are no secant terms present Convert one tangent-squared term to a secant-squared term. Expand and repeat if necessary. Case 4: Power in secant is odd and no tangent factors present Try integration by parts with the u being all secants except one and let dv be one secant term. Use the fact that ) sec( x | ) tan( ) sec( | ln x x dx + = . Case 5: If none of these guidelines apply Try converting to sines and cosines....
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This note was uploaded on 10/26/2008 for the course MATH 263A taught by Professor Keck during the Spring '08 term at Ohio University- Athens.

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