The answer seems to be wrong.
I do the following to numerically integral evaluation:
import numpy as np
import scipy as sp
import scipy.integrate
f=lambda x:np.sqrt(np.sin(x))
sp.integrate.quad(f,0.6,0.7)
get the following value:
0.07776347731181982
which matches with mathematica.
whereas
fI=sm.lambdify(z,sm.integrate(dydz(z)*tointegrate.subs(subdict)).subs(sm.exp_polar(2*sm.I*sm.pi),1.0))
and
fI(0.6)-fI(0.7)
gives:
mpf('-0.10638922100995812')
On Friday, July 6, 2012 12:00:19 PM UTC-4, pallab wrote:
>
>
>
> It seems sympy can not integrate sqrt(sin(x)).
>
> I did the following:
>
> import sympy as sm
> from sympy.abc import x,y,z
>
> tointegrate=sm.sqrt(sm.sin(y))
> sm.integrate(tointegrate)
>
> output is : Integral(sqrt(sin(y)), y)
>
> After a simple change of variable the integral is doable:
>
> def ytoz(z):
> return(sm.asin(z))
>
> def dydz(z):
> return(sm.diff(ytoz(z),z))
>
> subdict={y:cvytoz(z)}
> sm.integrate(dydz(z)*tointegrate.subs(subdict))
>
> output is : z**(3/2)*gamma(3/4)*hyper((1/2, 3/4), (7/4,),
> z**2*exp_polar(2*I*pi))/(2*gamma(7/4))
>
> best,
>
> Pallab
>
>
>
>
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