Question

Question #56d96

Answer 1

The integral does not converge.

Explanation:

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.