10sTrigInt - Math 142 Techniques of Integration...

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Math 142 Techniques of Integration Trigonometric Integrals · The book gives lots of rules/strategies . Read them but do NOT memorize. Use logic instead, as done below! · Recall the following natural pairings (in terms of derivatives): sin cos tan sec cot csc If the integrand does not contain natural pairings, then rewrite it so that it does. Eg: tan x cos 2 x = sin x cos x cos 2 x = sin x cos x . · Make a natural choice for s or t . For example, if the integrand involves sine and cosine, then try s = cos x ds = - sin x dx or t = sin x dt = cos x dx If the integrand involves tangent and secant, then try s = tan x or t = sec x . If the integrand involves cotangent and cosecant, then try s = cot x or t = csc x . · Then isolate off your ds or dt and try to express what is left in terms of just s or t . · The following will be helpful (and you must memorize them): sin 2 x = 1 - cos(2 x ) 2 and cos 2 x = 1 + cos(2 x ) 2 (half-angle formulas) cos 2 x + sin 2 x = 1 = cos 2 x cos 2 x + sin 2 x cos 2 x = 1 cos 2 x = 1 + tan 2 x = sec 2 x cos 2 x + sin
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