Looking for free online integration calculator.

[yungman]

I have been looking for an integration calculator. I need to solve

$$\int_0^{\pi} \frac{\cos (a \cos \theta)}{\sin \theta} d\theta$$

This is a sine integral that likely involve numerical analysis. I tried Wolfram free Mathematica and it did not find a solution. Please advice.

 

[dextercioby]

I suspect it has no closed form expression in terms of known special functions and you need to specify the range of the parameter, in order to study its convergence.

 

[Bill Simpson]

If you do not have any additional information about 'a' I suspect you are going to have little success.

If you know enough about the problem that you can justify integrating a series expansion then perhaps

In[1]:= Integrate[Series[Cos[a t]/Sin[t], {t, Pi/2, 6}], {t, 0, Pi}]

Out[1]= (Pi*(322560 - (-1 + a)*(1 + a)*Pi^2*(13440 - 168*(-5 + a^2)*Pi^2 + (61 - 14*a^2 + a^4)*Pi^4))*
Cos[(a*Pi)/2])/322560

But that is making several assumptions.

 

[yungman]

Thanks for the reply, "a" is just a constant, can be just a real number.

 

[yungman]

I suspect it has no closed form expression in terms of known special functions and you need to specify the range of the parameter, in order to study its convergence.

I already simplify the formula already. "a" is just a constant number, 0 ≤ $\theta$ ≤ $\pi$.

 

[krash661]

i typed,
" free online integration calculator ",
into google and received a list of them.
the first to come up was,

wolfram mathematic

 

[yungman]

i typed,
" free online integration calculator ",
into google and received a list of them.
the first to come up was,

wolfram mathematic

I tried that already, it can't calculate this function. But thanks.

 

[robphy]

Well... here's what I got from WolframAlpha...

www.wolframalpha.com/input/?i=integral%28+cos%28a*+cos%28x%29%29%2Fsin%28x%29%2C+x%29

as a definite integral... replacing the x argument by x=0..pi
says "integral doesn't converge"


Here's the integrand
www.wolframalpha.com/input/?i=%20cos%28a*%20cos%28x%29%29/sin%28x%29