How to integrate sqrt(P(sinx)), where P(x) is a polynom

asked 2012-05-10 11:44:54 +0100

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Hello! I'm trying to calculate a finite parametric integral, but with no success

sage: var('a,b,c')
(a, b, c)
sage: f = a*sin(x)^2+b*sin(x)+c
sage: f
a*sin(x)^2 + b*sin(x) + c
sage: var('A')               
sage: integrate(sqrt(f),x,-A,A)
integrate(sqrt(a*sin(x)^2 + b*sin(x) + c), x, -A, A)

Any help would be appreciated!

UPD: A < pi/2

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I think your question is not quite well-defined. It is difficult to determine the domain of `sqrt(f)`. For example, if a=1, b=1, c=0 then your integrand is not well-defined on the interval [-A, A] for any positive value of A.

benjaminfjones gravatar imagebenjaminfjones ( 2012-05-10 14:07:30 +0100 )edit