How do you evaluate the definite integral $int dx/(1-x)$ from $[-2,0]$ ?

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Answer 1 · 2018-05-01T02:11:12

$int_(-2)^0 \ 1/(1-x) \ dx ln 3$

We seek:

$I = int_(-2)^0 \ 1/(1-x) \ dx$

Noting that the integrand is continuous or over the range of integration, we can apply a simply substituting, Let

$u-1-x => (du)/dx = -1$

And we have a transformation of the integration limits:

$x = { (-2),(0) :} => u = { (3),(1) :}$

Thus we have:

$I = int_(3)^1 \ 1/u \ (-1) \ du$

$\ \ = int_(1)^3 \ 1/u \ du$

$\ \ = [lnu]_(1)^3$

$\ \ = ln 3 - ln 1$

$\ \ = ln 3$

How do you evaluate the definite integral int dx/(1-x)int dx/(1-x) from [-2,0][-2,0]?