Answer
$$0$$
Work Step by Step
Definition 5.4.3
\[
A=\lim _{n \rightarrow+\infty} \sum_{k=1}^{n} f\left(x_{k}^{*}\right) \Delta x
\]
$A=\lim _{n \rightarrow+\infty} \sum_{k=1}^{n}\frac{2}{n} \cdot \left(\frac{2 k}{n}-1\right)^{3} $
$x_{k}^{*}$ is the left endpoint, $f(x)=x^{3}, \Delta x=\frac{2}{n}$
Rewrite sum in closed form:
\[
A=\lim _{n \rightarrow+\infty} \frac{2 n^{2}}{n^{3}}
\]
Evaluate limit
\[
A=0
\]