# Sinc function definite integral

I have seen answers to similar questions that reference a Si(x) function as a solution to the integral of sinc(x). Most of these questions have infinite upper or lower limits, though. I am interested in the definite integral of the sinc-like function like below.

$$\int_{0}^{R}\frac{\sin(\frac{\pi r}{R})}{r}dr$$

Explanations for the use of Si(x) lead me in circles. Could anyone explain if Si(x) is necessary here and how it is used.

• This one is just a sinus, not a cardinal sinus, there is no $r$ at denominator... – zwim Oct 7 '17 at 2:33
• Yes, it is necessary to have $\operatorname{Si}(x)$ here. That is why this special function is defined :) – Sangchul Lee Oct 8 '17 at 19:24
• Sorry I am unfamiliar with Si(x). Would this integral just become Si(pi)? – peasqueeze Oct 8 '17 at 19:43
• Yes, it's value is simply $\operatorname{Si}(\pi)$, independent of $R$. – Sangchul Lee Oct 8 '17 at 20:32