Question

Find the area bounded by $x-axis$, the curve $y=x^3$ and the lines $x=-a$ and $x=a$.

Answer 1

$A={\int }_{-a}^a{x}^{3}dx$

$\Rightarrow {\left[\frac{x^4}{4}\right]}_{-a}^a$

$\Rightarrow \frac{a^4}{4}-(-\frac{a^4}{4})=\frac{a^4}{2}$.