1,205 views
1 votes
1 votes
Evaluate the following definite integral :

$\int \limits_0^1 \log \left(\frac{1}{x} - 1 \right)$

3 Answers

Best answer
3 votes
3 votes
Applying the property of logarithms:

$log(\frac{1}{x}-1) = log(\frac{1-x}{x}) = log(1-x) - log(x)$

Integrating from 0 to 1 we can see that the same values are repeated in each term thus reducing the answer to zero.
selected by
0 votes
0 votes
ans is 0
still i want to cnfirm
xlg((1/x)-1)-log(1-x)
on putting x=0 /////     lg((1/x)-1) this will be undefined

Related questions

1 votes
1 votes
1 answer
1
ankitgupta.1729 asked Jun 11, 2018
910 views
$\displaystyle S = \int_{0}^{2\pi } \sqrt{4\cos^{2}t +\sin^{2}t} \, \, dt$Please explain how to solve it.
1 votes
1 votes
1 answer
2
Ayush Upadhyaya asked Oct 13, 2018
733 views
What is the value of $\int_0^\pi log(1+cosx)dx$
1 votes
1 votes
0 answers
3