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

integralsin(x)/x

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!

Best Answer

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 .
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