# Homework Help: Find where an improper integral converges

1. Oct 19, 2012

### rocapp

1. The problem statement, all variables and given/known data

-∞(dx/x2)

2. Relevant equations

3. The attempt at a solution

∫(dx/x2) = -1/x

(-1/∞) - (-1/-∞) = 0

However, the answer is that the integral diverges. Why is this the case?

2. Oct 19, 2012

### jbunniii

The function $1/x^2$ grows infinitely large as $x \rightarrow 0$, so you have to break this into two improper integrals:
$$\int_{-\infty}^{0} dx/x^2 + \int_{0}^{\infty} dx/x^2$$
You can easily check that both of these integrals diverge to $\infty$.

3. Oct 21, 2012

### rocapp

Thanks! I forgot that it was dependent on the function being continuous.

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