The area bounded by the curve $y=x^{3}$, the $\mathrm{X}$ -axis and the lines $x=1$ and $x=4$ is
The area bounded by the curve $y=x^{3}$, the $\mathrm{X}$ -axis and the lines $x=1$ and $x=4$ is
$\frac{127}{4}$ sq. units
64 sq. units
27 sq. units
$\frac{255}{4}$ sq. units
Solution
Required area is shaded.
$\begin{aligned}
\text { Area } &=\int_{1}^{4} x^{3} d x=\left[\frac{x^{4}}{4}\right]_{1}^{4} \\
&=\frac{1}{4}\left[4^{4}-1\right]=\frac{1}{4}(256-1)=\frac{255}{4} \text { sq. unit }
\end{aligned}$
