An Elliptic IntegralDate: 01/05/2003 at 08:52:03 From: Rajiv (i am in college) Subject: Integration Integrate Sqrt[Sin[x]] I tried to solve this problem using the usual approaches, but they do not seem to work. It seems that the problem can be solved only by applying some trick or technique. One of my friends suggested that it can be solved by using Laplace transform, but I could not solve it that way. Date: 01/07/2003 at 14:09:19 From: Doctor Wilkinson Subject: Re: Integration Interesting problem, Rajiv! Doing the substitution t = tan(x/2) reduces this integral to the integral of (2t/(1+t^2))^(1/2) (1+t^2)^(-1) and this is an elliptic integral. It cannot be expressed in terms of elementary functions, but can be expressed in terms of the inverses of the Jacobian elliptic functions (with a bit of work). The same applies to the integrals of the square root of cosx or tanx. - Doctor Wilkinson, The Math Forum http://mathforum.org/dr.math/ |
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