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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.

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

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