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Section7.3-Trigonometric+Substitution

# Section7.3-Trigonometric+Substitution - WhenToUse 1 9 x 2...

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9/3/2013 1 Section 7.3 Trigonometric Substitution When To Use? 2 9 x dx 2 1 25 dx x 1 3 2 0 4 x x dx The method of trig substitution recommends a substitution that rationalizes the integrand in cases like these. Example 2 9 x dx 3sin 3cos Substitute x dx d   2 9 9sin 3cos d 2 9 1 sin 3cos d 2 9cos 3cos d  3cos 3cos d 2 9cos d   9 1 cos2 2 d 9 1 sin 2 2 2 C Now resubstitute. Example continued 9 1 sin 2 2 2 C We know: 1 3sin sin 3 sin 3 x x x What is: ? sin 2 θ sin 3 x 1 2 9 1 9 sin 2 sin 9 2 2 2 3 9 x x C x C x 3 2 9 x 2 2 9 cos 3 2 sin 2 2sin cos 9 9 x x x

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Section7.3-Trigonometric+Substitution - WhenToUse 1 9 x 2...

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