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

[suvadip]

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

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

 

[chisigma]

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]

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 .