Hello, I have a partial answer and perhaps you found a bug in
elliptic_e in Sage (read below).
To evaluate the integral do something like this (note replacing A by
lowercase letter)
T,r,a,b=var('T r a b')
F(x)=integrate(sqrt(1+r*sin(x)^2),x, algorithm='mathematica_free')
eq = T==F(b)-F(a)
eq
the answer is
T == -elliptice(a, -r) + elliptice(b, -r)
Sage parsed the answer badly :(. If in compare the definition of
eliptice ( http://mathworld.wolfram.com/EllipticIntegraloftheSecondKind.html
) and elliptic_e in sage, this should be
T == -elliptic_e(a, -sqrt(r)) + elliptic_e(b, -sqrt(r))
in Sage. (I think, but I would be happy if someone familiar with
special functions confirms this. If I compare numerical approximation
of elliptice(0.5, 0.1) in wolfram aplha and elliptic_e(0.5, 0.1) from
help for elliptic_e in Sage, they are equal! So what is correct? Is
the definition of ellitpic_e in harmony with actual implementation?)
Put values for a,b and T and find r numerically.
Robert Marik
On 23 led, 05:48, John H Palmieri <[email protected]> wrote:
> I have an equation
>
> T = integral from a to b of sqrt(1+A*sin^2(x)) dx
>
> where I know T, a, and b, but I don't know A. Can I use Sage to solve
> this?
>
> (I happen to know that A is close to zero, so I can replace the
> integrand by a Taylor polynomial (in terms of A) and then integrate
> that, but is there another way?)
>
> --
> John
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