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.