# How to integrate sinc function numerically [closed]

How to compute (numerically)

$$F(x) = \int_{-\infty}^x \dfrac{\sin(t)}{t} dt$$

• Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc. Commented Jan 20, 2021 at 3:53
• @KingLogic $F(x)$ is the source function for the PDE that I am solving (numerically). I just need to compute $F(x)$ to solve the PDE (that is part of wave propagation simulation code). Commented Jan 20, 2021 at 3:58
• Start by breaking up the integral into the regions $(-\infty, 0)$ and $(0, x)$, then over $(x, \infty)$. Commented Jan 20, 2021 at 3:59
• Consider the Taylor series of $\sin t$ Commented Jan 20, 2021 at 4:08

$$F(x) = \int_{-\infty}^x \dfrac{\sin(t)}{t} dt=\text{Si}(x)+\frac{\pi }{2}$$

For the computation of the sine integral function, you will find subroutines in Numerical Recipes (have a look here).