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Ammar Durghalli
03/31/08 01:36am

I'm almost always having trouble evaluating trigonometric integrals using Mathematica. Some integrals are even easy to do by hand, yet Mathematica is unable to provide an elegant answer-if any!

For example, This integral is used to normalize the solutions to the theta-laplacian equation. I tried to evaluate:

Integrate[Sin[x]^(2 n+ 1),{x,0,Pi}]and this is what came out:

If[Re[n]>-1, -(Pi^3/2 Csc[n Pi])/((Gamma(-n)(Gamma(n+3/2))),Integrate[Sin[x]^(2 n+ 1),{x,0,Pi}]]. If you try to evaluate this output for,say n=2, you get a complex infinity error..

The answer in the book is given (from tables I'm sure) as 2^(2 n +1)(n!)^2/(2 n +1)!

I'm I not entering the integral correctly, or is Mathematica unable to compete with ancient tables of integration?

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Subject (listing for 'Definite trig. integrals')
Author Date Posted
Definite trig. integrals Ammar Durgha... 03/31/08 01:36am
Re: Definite trig. integrals Xavier 04/14/08 06:16am
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