3 views

A $5$-point sequence $x[n]$ is given as
$x[-3]=1, \quad x[-2]=1, \quad x[-1]=0, \quad x[0]=5, \quad x[1]=1 .$
Let $X\left(e^{j \omega}\right)$ denote the discrete-time Fourier transform of $x[n]$. The value of $\int_{-\pi}^{\pi} X\left(e^{j \omega}\right) d \omega$ is

1. $5$
2. $10 \pi$
3. $16 \pi$
4. $5+j 10 \pi$