- #1
Sistine
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Homework Statement
I'm trying to prove the following definite integral of [tex]sinc(x)[/tex]
[tex]\int_{-\infty}^{\infty}\frac{\sin(x)}{x}dx=\pi[/tex]
Homework Equations
The Attempt at a Solution
I've tried power series expansions as well as trigonometric identities like
[tex]\frac{\cos 2x}{x}=\frac{\cos^2 x}{x}-\frac{\sin^2 x}{x}[/tex]
I also looked at techniques used to integrate the definite integral
[tex] \int_{-\infty}^{\infty}e^{-x^2}dx [/tex]
which I know is solved by double integration and changing to polar coordinates. However, this does not help me integrate [tex]sinc(x)[/tex].