Answer
$$\int_0^{\frac{\pi}{2}}\int_0^1y\cos{x}\hspace{0.5mm}dydx=\frac{1}{2}$$
Work Step by Step
We will start with the integral with respect to y:
$\int_0^{\frac{\pi}{2}}\int_0^1y\cos{x}\hspace{0.5mm}dydx=\int_0^{\frac{\pi}{2}}\left(\frac{y^2}{2}\cos{x}\right)\bigg\vert_0^1dx$
$=\int_0^{\frac{\pi}{2}}\frac{1}{2}\cos{x}dx=\frac{1}{2}\sin{x}\bigg\vert_0^{\frac{\pi}{2}}=\frac{1}{2}-0=\frac{1}{2}$
