Find the area between the line y= x and y = x^2

To find the area betwen  y = x and
x^2.

The intersection points of y = x and y = x^2  is given
by:

x= x^2.

Or x-x^2 =
0.

 Or x(1-x) = 0.

So x= 0 , Or 1-x = 0
, Or x = 1.

So the area between  curves is to be found from x= 0 to
x = 1.

If we draw the graph , y = x  is above x = x^2 from x= 0 to x
= 1 .

Therefore  area  between y = x and y =x^2 is given
by:

Area = Integral (x-x^2)dx from x= 0 to x =
1.

Area = {(x^2/2 -x^3/3 at  x= 1} - {(x^2/2 -x^3/3 at  x=
0}

Area = { 1/2-1/3}- 0

Area = (3-2)/6
= 1/6.

Therefore the area between the curves = 1/6 sq
units.