Split the integral up
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Let's do the second integral on the right.
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Therefore, the integral is divergent.
Why is this integral divergent?:
I get 1/2 * (ln 1 - ln(inf) + ln(inf) - ln 1) so I thought the answer would be zero. Or do we assume that the infinities are different in each ln therefore it diverges? Or am I completely off?
Any input would be greatly appreciated!
Thanks in advance!
[/tex]lim_{a\to\infty}\int_{-a}^a f(x)dx[/tex] is often called the "Cauchy Principal Value" of and often exists when the integral itself, which is defined as does not exist.
Here, the integral intself, where the two limits must be taken independently does not exist- what you calculated is the "Cauchy Principal Value".