Question

Find the area between the curves y=x and y=x2

Answer 1

The required area is represented by the shaded area OBAO as

The points of intersection of the curves,y=x and y=x2,is A(1,1).

We draw AC perpendicular to x-axis.

∴Area(OBAO)=Area(ΔOCA)-Area(OCABO)...(1)

=

$\int_{0}^{1} x \,dx$

$-\int_{0}^{1} x^2 \,dx$

=[$\frac{x^2}{2}$]10-[$\frac{x^3}{3}$]10

=$\frac{1}{2}$-$\frac{1}{3}$

=$\frac 16$units