GATE Electronics and Communications (EC) 2021 Solved Paper

Consider the signals x[n] = 2^n-1 u[-n + 2] and y[n] = 2^-n+2 u[n + 1], where u[n] is the unit step sequence. Let X(e^jω) and Y(e^jω) be the discrete-time Fourier transform of x[n] and y[n], respectively. The value of the integral
$\frac{1}{2\mathit{\pi }}{\int }_0^{2\mathit{\pi }}\mathit{X}\left({\mathit{e}}^{\mathit{j}\mathit{\omega }}\right)\mathit{Y}\left({\mathit{e}}^{-\mathit{j}\mathit{\omega }}\right)\mathit{d}\mathit{\omega }$
(rounded off to one decimal place) is _____