Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Integral Calculus
0 votes

Integrate : $\int \limits_0^{\infty} \large\frac{\log x}{1+x^2}$$dx$

\[\begin {array} {1 1} (a)\;0 \\ (b)\;-1 \\ (c)\;1 \\ (d)\;2 \end {array}\]

Can you answer this question?

1 Answer

0 votes
Put $ x= \cot \theta$
$dx= -cosec ^2 \theta.d\theta$
$x=0, \theta=\large\frac{\pi}{2}$
$x=\infty, \theta=0$
$\int \limits^0_\frac{\pi}{2} \large\frac{\log \cot \theta}{1+\cot^2 \theta} $$(- cosec^2 \theta)d \theta$
By using property
$\int \limits^0_\frac{\pi}{2} \log \cot \theta.d \theta$
Hence a is the answer.
answered Dec 13, 2013 by meena.p
Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App