Question

The area of the region bounded by the curve $y=x^2$ and $y=4x-x^2$ is

• A. $\frac{16}{3}sq.units$
• B. $\frac{8}{3}sq.units$
• C. $\frac{4}{3}sq.units$
• D. $\frac{2}{3}sq.units$

Answer 1

The correct option is B $\frac{8}{3}sq.units$

Here area,

${\int }_0^2(4x-x^2-x^2)dx$

$={\int }_0^2(4x-2x^2)dx$

$={(2x^2-\frac{2}{3}{x}^3)}_0^2$

$=\frac{8}{3}$