- #1

krindik

- 65

- 1

## Homework Statement

[tex]\int_{-\infty}^{\infty} \, \frac{\sin{x}}{x} \, dx[/tex]

Could u pls advice me with the procedure to follow not only the answer?

## The Attempt at a Solution

1. Use complex numbers as there is a pole of order=0 at x=0

[tex]

\int_{-\infty}^{\infty} \! f(x) \, dx = 2\pi\, i \sum_{res\, upper\, hp} {f(x)} \, + \pi\, i \sum_{res\, real\, axis} {f(x)}

[/tex]

which give 0 as the answer

2. Expand by sin(x) by Taylor series around 0 and multiply by x this gives a divergent series

Couldn't figure out which is correct?

Thanks