I was learning Fourier Transform recently, and I came across this question. Although I know how to complete the Fourier transform for a function, but how do you evaluate another integral with the known Fourier Transform? Question as follows: Find the Fourier Transform for this function:
$y(x)=\left\{ \begin{array}{cc} \pi ,& \left |x \right | < 1\\ 0,& \left | x \right | > 1 \end{array} \right.$
Hence Evaluate the integral:
$\int_{-\infty}^{\infty}\frac{sinx}{x}\,dx\,.$
and also:
$\int_{-\infty}^{\infty}\frac{\sin^2x}{x^2}\,dx\,.$
From what I understand, Symmetry property of Fourier Transform may help!