Tuesday 5 February 2019

integration - $int^infty_0frac{sin x}{x} , dx = frac{1}{2i}int^infty_{-infty} frac{e^{ix}-1}{x} , dx$, why?

How comes this true?




$$\int^\infty_0\frac{\sin x} x \, dx = \frac{1}{2i}\int^\infty_{-\infty} \frac{e^{ix}-1} x \, dx$$

No comments:

Post a Comment

real analysis - How to find $lim_{hrightarrow 0}frac{sin(ha)}{h}$

How to find $\lim_{h\rightarrow 0}\frac{\sin(ha)}{h}$ without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...