Question

The area (in sq. units) bounded by the curve $y=max.\left(x^{3} , x^{4}\right)$ and the $x$ -axis from $x=0$ to $x=1$ is

Answer 1

$\max \left(x^{3}, x^{4}\right)=x^{3}(\forall x \in(0,1))$
$\therefore $ Required area $=\displaystyle \int _{0}^{1} x^{3} d x = \left(\frac{x^{4}}{4}\right)_{0}^{1} = \frac{1}{4}=0.25$ sq. units