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