Answer
The integral converges and its value is $3 * 4^{1/3}.$
Work Step by Step
We have
$$
\int_{0}^{4} \frac{d x}{x^{2/3}}= \int_{0}^{4}x^{-2/3}dx\\
=\frac{1}{1/3}x^{1/3}|_0^{4}=3(4^{1/3}-0)=3 * 4^{1/3}.
$$
Hence, the integral converges and its value is $3 * 4^{1/3}.$
