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MATH 152 -
8_3
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1 8.3: Trig SubstitutionRecall: Compute the following derivatives:ddxsin−1xa=ddxtan−1xa=ddxsec−1xa=These derivatives are the keys to using trig substitutions to integrate. When necessary, use the followingchart to guide you in making trig substitutions:If the integral contains a power of: Then use the following substitution:a2− x2x2+ a2x2− a2As with inverse trig functions, reference triangle can be especially useful in your substitution.Examples:ˆ2−2p4 − x2dx =1ˆx3√4x2− 9dx =On Beyond Average:ˆx2√9 − x2dx =ˆ1√x2− 2x + 5dx
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