Welcome to our community

Be a part of something great, join today!

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

suvadip

Member
Feb 21, 2013
69
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
Feb 13, 2012
1,704
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
Jan 17, 2013
1,667
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 .