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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: /0 on May 19, 2009, 11:50:05 am

Title: integral
Post by: /0 on May 19, 2009, 11:50:05 am: Solve for x: $\int \sqrt{\sin{x}} dx$ :buck2:

thnxxx
Title: Re: integral
Post by: TrueTears on May 19, 2009, 04:46:40 pm: No elementary solutions.
Title: Re: integral
Post by: dcc on May 19, 2009, 09:46:35 pm: 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 $x \in (0, \pi)$ .