Answer
Diverges, $\infty$
Work Step by Step
Evaluate the improper integral and see if it converges or diverges
$\int ^{\infty} _1 \frac{3}{\sqrt[3] x} dx$
Rewrite the integral
$\lim\limits_{b \to \infty} \int^b_1 \frac{3}{\sqrt[3] x} dx$
$\lim\limits_{b \to \infty} [\frac{9}{2}x^{\frac{2}{3}} ]^b_1 $
$\lim\limits_{b \to \infty} (\frac{9}{2} b^{\frac{2}{3}} - \frac{9}{2})$
Evaluate the limit
$\infty - \frac{9}{2}$
$\infty$ , Diverges
