# Comparison Theorem and Limits of integration

1. Apr 8, 2013

### Painguy

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

Why is it that when using the comparison theorem my limits of integration must be from a constant value to infinity and not from negative infinity to infinity?

For example ∫ x/(1+x^2) dx from -∞ to ∞

2. Apr 8, 2013

### jbunniii

Can you be more specific about what comparison theorem you are talking about?

For your example, notice that if $x \geq 1$, you can easily check that
$$\frac{x}{1+x^2} \geq \frac{1}{2x}$$
What does that tell you?

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