For the expansion I need the value of the integral of $a_o$ = $\frac{1}{2\pi} \int_{-\pi}^\pi \frac{\sin{x}}{x} dx$. But I can't find an easy understandable way to integrate it. Instructor asked to do an inproper integral, but I couldn't. Can anyone here assist me how to exactly to it?
Asked
Active
Viewed 49 times
0
-
Scroll down the WP page on the sinc function. You need to learn about the so called sine integral. In other words, the Fourier coefficients of this function cannot be written in terms of elementary functions (unless you include the sine integral among them :-). It is one of the first elementary functions without an elementary indefinite integral a calculus student is likely to encounter. – Jyrki Lahtonen Nov 24 '23 at 17:39
-
Type in the integrals to Wolfram Alpha (or Mathematica, or some other CAS, if available) to see what it spews out. – Jyrki Lahtonen Nov 24 '23 at 17:40