Show \[ \int_{(0, \infty)} {\sin(x) \over x }\dx = {\pi \over 2} .\]
Solution
Take an indented semicircle. Let \(I\) be the original integral, then \[ I = {1\over 2i} \int_\RR {e^{iz} - 1 \over z } \dz .\]
Sinc Function
E-PMURO
- Area
- Complex Analysis
- Topics
- Contour Integration, Integrals, Residues
- Status
- draft