Draw a rough sketch of the curves y=sin x and y=cos x, as x varies from 0 to, and find the area of the region enclosed between them and the x-axis.

Given

• First curve y = cos x

• Second curve y = sinx

• x= 0

•

Consider the curves y = cosx and y = sin x

Now consider the y values for some random x values between 0 and for the functions y = cos x and y = sin x.

From the above table we can clearly draw the below graphs.

The required area under the curve is given by:

Area of OAD = Area under the curve OA + Area under the curve AD

[using the formula, and ]

Thus the area under the curves y = cos x and y = sin x is 2 - √2 sq. units.