Question

How do you evaluate the integral `int 1/x` from `[-oo,-1]`?

Answer 1

The integral:

`int_(-oo)^(-1) (dx)/x`

is not convergent.

Explanation:

This is an improper integral that is evaluated as:

`int_(-oo)^(-1) (dx)/x = lim_(t->-oo) int_t^(-1) (dx)/x`

The indefinite integral is:

`int (dx)/x = lnabs(x)+C`, so:

`int_(-oo)^(-1) (dx)/x = lim_(t->-oo) (ln(1) - ln abs(t)) = lim_(t->-oo) -ln abs(t) = -oo`