I have been working on getting an analytical equation for a scalar potential of a source function in an elastic wave equation, in which I end up with an expression that has an integration of unnormalized $Sinc$ function in an interval as:
$\int\limits_{-\pi a}^{\pi a} Sinc(x\:k) \:dk$
here $a$ is a constant and $x$ is a spatial domain and $k$ is corresponding spatial frequency (Wavenumber). I know the integration of $Sinc$ function is $\pi$ in the integral between $-\infty$ and $\infty$. But I don't know how to integrate $Sinc$ in an interval between $-\pi a$ and $\pi a$.
Anyway I did try to simplify the integration as follows.
$2\:\int\limits_{0}^{\pi a} Sinc(x\:k) \:dk$
$2\:Si(\pi a)$ $\;$ where $Si$ is a sine integral.
I just wanted to know if I am right, if not please help me to simplify the integration. Many thanks in advance.