Integral (1/x^n): Convergence/Divergence Rules

[dami]

Homework Statement

give a general rule for when Integral (1/x^n) from (x, 0, a), a>0 converges or diverges.

Homework Equations

The Attempt at a Solution

I have checked the textbooks for this answer but i can't seem to find it. The closest i got was Integral (1/x^n) from (x, 1, infinity), converges or diverges.

 

[Mark44]

Homework Statement

give a general rule for when Integral (1/x^n) from (x, 0, a), a>0 converges or diverges.

Homework Equations

The Attempt at a Solution

I have checked the textbooks for this answer but i can't seem to find it. The closest i got was Integral (1/x^n) from (x, 1, infinity), converges or diverges.

The integral is $$\int_0^a \frac{dx}{x^n}~=~\int_0^a x^{-n}dx$$

Instead of searching textbooks for the answer, why don't you work it out? Note that this is an improper integral, so you'll need to use limits.