Question #56d96

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Answer 1 · 2017-02-26T18:30:25

The integral does not converge.

The integrand is undefined at $x = 0$ which is in the interval of integration.

Therefore, we must split the integral into two improper integrals.

$int_-1^1 (1/x) dx = int_-1^0 (1/x) dx + int_0^1 (1/x) dx$ provided that the two integrals on the right converge.

Neither integral on the right converges, but it is sufficient to show that one of them fails to converge.

$int_0^1 (1/x) dx = lim_(ararr0^+) int_a^1 (1/x) dx$

$= lim_(ararr0^+) {: lnx]_a^1$

$= lim_(ararr0^+) (ln1 - lna)$

$= lim_(ararr0^+) lna = -oo$

So the integral does not converge.