Numerical integral of sin(x)/x from 0 to inf

I am using a loop to estimate the parameters in a formula. However, when using the syntax 'integral' to numerically integrate sin(x)/x from 0 to inf, Matlab always gives me a warning and a wrong answer. The exact result of this integral is pi/2 if I use the syntax 'int'. Unfortunately, for estimation purpose, numerical integration saves me a great deal of time, and I can only use 'integral' rather than 'int'. My formula is pretty similar to the problem of integrating sin(x)/x. Can anyone help me correct the result given by Matlab 'integral'? Many thanks!

Answer 1

[Star Strider]

One option is to use a large upper limit that is less than Inf:

z = integral(@(x) sin(x)./x, 0, 1E+4)
z =
          1.57089154538596 

That is reasonably close to .

[Livvy Zhen]

Thanks! I have tried that before. But this function is just for demonstration. My formula is similar to it and this setup will greatly slow down my estimation. I am wondering if Matlab could use a more robust way to calculate the numerical integral.

[Star Strider]

My pleasure.

Please post the function you want to integrate, as well as any additional information as necesary. It may be possible to use the 'Waypoints' name-value pair to help approximating it. With the necessary information, we may be able to help you with it.

Answer 2

[madhan ravi]

y=@(x)sin(x)./x
integral(y,0,inf)

[Livvy Zhen]

Thanks! But that is not working on my Matlab 2016a. Matlab always gives me the wrong answer. Is it working on your Matlab? If yes, I might need to change the version.

[madhan ravi]

what error are you getting? Below is the warning I got

Warning: Reached the limit on the maximum number of intervals in use.
Approximate bound on error is   4.9e+00. The integral may not exist, or it may
be difficult to approximate numerically to the requested accuracy. 
> In integralCalc/iterateScalarValued (line 372)
  In integralCalc/vadapt (line 132)
  In integralCalc (line 83)
  In integral (line 88)

[Livvy Zhen]

Warning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is 4.9e+00. The integral may not exist, or it may be difficult to approximate numerically to the requested accuracy.

[madhan ravi]

So the error message is really clear " it is difficult to approximate numerically"

[Livvy Zhen]

That is why I am posting this question. This numerical integral works well on other softwares.