Convergence of Improper Integral with Limit Evaluation

[flyingpig]

Homework Statement

Determine whether the improper integral diverge or converge. If it is convergent, evaluate it with a limit

$$\int_{0}^{1}\frac{1}{\sqrt[3]{x}}dx$$Just from inspection, I thought this was a p-series with 1/3 < 1, but then I noticed the limits of integration is from 0 to 1.

So my question is, is there a way, just from inspection, to notice this is convergent without resorting to any test?

 

[flyingpig]

Just fixed question

 

[Dick]

It's not a p-series. It's not any kind of series at all. It's an improper integral. Integrate it and take the limit as the lower limit approaches 0.

 

[SammyS]

It's not a p-series. It's not any kind of series at all. It's an improper integral. Integrate it and take the limit as the lower limit approaches 0.

I.E. Evaluate:

$$\int_{a}^{1}\frac{1}{\sqrt[3]{x}}dx$$

Take the limit of the result as a → 0⁺.