see the diagram for the curves on the graph.
For the area enclosed by y = Sin x and y = cos x and the coordinate axes between x = 0 and π/2, we need to do integration wrt x.
[tex]Area= \int\limits^{\pi/2}_0 {y} \, dx\\\\=\int\limits^{\pi/4}_0 {Sin\ x} \, dx+\int\limits^{\pi/2}_{\pi/4} {Cos\ x} \, dx\\\\=[-cos\ x]_0^{\pi/4}+[Sin\ x]_{\pi/4}^{\pi/2}\\\\=1-\frac{1}{\sqrt2}+1-\frac{1}{\sqrt2}\\\\=2-\sqrt2[/tex]
