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MATH 152 -
8_2
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1 8.2: Trig IntegralsBy now, you should be able to integrate the basic trig functions and know the appropriate identitiesfor integrating the squares of the trig functions:ˆsin x dx =sin2x = .ˆcos x dx =cos2x = .ˆtan x dx =tan2x = .ˆcot x dx =cot2x = .ˆsec x dx =sec2x = .ˆcsc x dx =csc2x = .1To integ rate higher powers of tr ig functions, the key is, if possible, to “save” a derivative du of a trigfunction u and rewrite the rest of the integral in terms of u.Examples:ˆsin3xcos xdx =ˆtan7x sec3x dx =2ˆcsc44x dx =ˆsin4x dx =3Key Identities to Compute Product-to-Sum Integrals:sin(A ± B) =cos(A ± B) =These are extremely imp ortant in the study of Partial Differential Equations.Examples:Computeˆsin(3x) sin(5x) dx.Computeˆπ−πsin(3x) cos(5x)
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