The area bounded by the y-axis, y=cosx and y=sinx when 0≤x≤(π )/2 is :

The correct answer is Option (4) → $(\sqrt{2} - 1) sq.units$

Required area = $\int\limits_0^{\pi/4}\cos x-\sin x\,dx$

$=\left[\sin x+\cos x\right]_0^{\pi/4}$

$=\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}-1-0$

$=\sqrt{2}-1$