Integration of log(1-x) from 0 to 1

Member
How to evaluate $$\displaystyle \int^1_0 log(1-x) dx$$

I am confused as log is not defined at 0. Please help

chisigma

Well-known member
How to evaluate $$\displaystyle \int^1_0 log(1-x) dx$$

I am confused as log is not defined at 0. Please help
The fact that ln x is undefined for x=0 has no importance... what You have to do is computing...

$\displaystyle \lim_{t \rightarrow 1} \int_{0}^{t} \ln (1-x)\ dx$

Kind regards

$\chi$ $\sigma$

ZaidAlyafey

Well-known member
MHB Math Helper
How to evaluate $$\displaystyle \int^1_0 log(1-x) dx$$

I am confused as log is not defined at 0. Please help
This is an improper integral which might converge or diverge. You can use integration by parts to solve it .