Draw a rough sketch of the curves `y =sin x `and `y=cos x` varies from 0 to `pi/2` and find the area of the region enclosed by them and x-axis

Explanation

Given curves `y =sin x `and `y=cos x` varies from `0` to `pi/2`
so, required area,
`=int_0^(pi/4)(sin x)dx+int_(pi/4)^(pi/2)[(cos x)dx`
`=[-cos x]_0^(pi/4)+[sinx]_(pi/4)^(pi/2)`
`=[-1/sqrt2+1]+[1-1/sqrt2]`
`=2-sqrt2` sq.units