Question

Why is it that from 1 to inf, the area under 1/x^2 is finite but the area under 1/x is infinite?

Answer 1

1/x does not converge to 0 fast enough.\[\int\limits_{1}^{\infty} \frac {dx}{x} = \lim_{k \rightarrow \infty} \left[ \ln x \right]_{k}^{1} = \ln \infty - \ln 1 = \infty\]

Answer 2

Oops, the 1 and k are supposed to be switched on the limit step.

Answer 3

Ah, I still understand your point. Thanks!