Question

Roughly sketch the region enclosed by the curves y = sin x, y = cos x and the x - axis
between x = 0 and x = π 2/ . Also find the area of this region.

Answer 1

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.
 

$Area= \int\limits^{\pi/2}_0 {y} \, dx\\\\=\int\limits^{\pi/4}_0 {Sin\ x} \, dx+\int\limits^{\pi/2}_{\pi/4} {Cos\ x} \, dx\\\\=[-cos\ x]_0^{\pi/4}+[Sin\ x]_{\pi/4}^{\pi/2}\\\\=1-\frac{1}{\sqrt2}+1-\frac{1}{\sqrt2}\\\\=2-\sqrt2$