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Topic: integration cube root sin x
Replies: 5   Last Post: Feb 28, 2013 5:09 AM

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Doug Magnoli

Posts: 767
Registered: 12/6/04
Re: integration cube root sin x
Posted: Jul 22, 2001 1:29 AM
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Are you talking about an indefinite or a definite integral? In case of
the definite integral from 0 to pi/2, the beta function will give you a
solution.

If I remember right, B(n,m) = 2 Int[0, pi/2, (sin x)^(2n-1) (cos
x)^(2m-1) dx]

So int[0, pi/2, sinx^(1/3) dx] = (1/2) B(1/2, 2/3) = gamma(1/2)
gamma(2/3) / gamma (7/6)

~ 2.587

-Doug Magnoli


Tim 9-23 wrote:

> Can this be expressed in elementary functions? I doubt it.
>
> My email address is anti-spammed. If you want to email me,
> remove the 2 B's after hitting email reply.
>
> Tim 9-23








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