integral

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/0

Victorian
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integral

« on: May 19, 2009, 11:50:05 am »

0

Solve for x: $\int \sqrt{\sin{x}} dx$ :buck2:

thnxxx

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TrueTears

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Re: integral

« Reply #1 on: May 19, 2009, 04:46:40 pm »

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No elementary solutions.

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dcc

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Re: integral

« Reply #2 on: May 19, 2009, 09:46:35 pm »

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Quote from: /0 on May 19, 2009, 11:50:05 am

Solve for x: $\int \sqrt{\sin{x}} dx$ :buck2:

thnxxx

Note that $\sqrt{\sin x} \approx x - \frac{x^{\frac{5}{2}}}{12} + \frac{x^{\frac{9}{2}}}{1440}$

Hence $\int \sqrt{\sin x} \ dx \approx \frac{x^{\frac{3}{2}}}{55440} \left( 7x^4 - 1320x^2 + 36960) + C$

I think you'll find this is a fairly reasonable approximation for $x \in (0, \pi)$ .

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