Integrating product of bessel function,

[thomitsu]

Hallo there. I m trying to integrate a bessel function but with no great success... I thing it can't be calculated..
I m trying to simulate the airy pattern of a certain aperture radius and wavelength in matlab.

the integral is : int (besselj(1,16981.9*sin(x)))^2/ sin(x) dx

where you can change 1/sinx to csc(x) so the integral becomes

int csc(x)*(besselj(1,16981.9*sin(x)))^2 dx x from 0 to 0.0002257

the problem is that there is dx and not d(sinx) ( it whould be easy then..)

any ideas how can I do this??


thanks in advance!

 

[JJacquelin]

You just have to use numetical integration
http://www.wolframalpha.com/input/?...1.9*sin(x)))^2+/sin(x)+dx+from+0+to+0.0002257

 

[thomitsu]

:):):)

thank you!