Find the area bounded by the curve `y = sin x` between `x = 0` and `x=2pi` .

Explanation

The given curve is `y=sin x`
Some values of x and the corresponding values of y are given below :

Taking a fixed unit (distance ) lfor `pi` along the x-axis , we can plot the points `(0,0) (pi/6,1/2),(pi/2,1),(pi,0)(3pi/2,-1) and (2 pi , 0)`
Join these points freehand to obtain a rough sketch of the given curve.

Required area = (area OABO ) + (area BCDB)
`= overset(pi)underset(0)(int) y ` dx + `overset(2pi)underset(pi)(int) (-y) dx [because` area BCDB is below the x-axis ]
`= overset(pi)underset(0)(int) sin x dx - overset(2pi)underset(pi)int sin x dx `
`= [-cos x]_(0)^(pi) - [-cosx ]_(pi)^(2pi) = (2 + 2) = 4` sq units
Hence , the required area is 4 sq units.