Answer
$\dfrac{\pi}{2}-1$
Work Step by Step
Our aim is to solve the integral $ \int_0^{\pi/2} x \cos x dx$
Use integration by parts formula.
$ \int x \cos x dx =x \sin x -\int \sin x \ dx \\= x \sin x + \cos x+C$
Now, $ \int_0^{\pi/2} x \cos x dx=[x \sin x + \cos x+C]_0^{\pi/2}\\=[\dfrac{\pi}{2}+0]-[1] \\=\dfrac{\pi}{2}-1$
