Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Provide solution for RD Sharma maths class12 Chapter Definite Integrals exercise 19.2 question 45.

Provide solution for RD Sharma maths class12 Chapter Definite Integrals exercise 19.2 question 45.

Answers (1)

Answer  : \frac{\log2}{1+\log 2}

 Hint   : use indefinite formula and the limit to solve this integral

 Given : \int_{1}^{2}\frac{1}{x(1+\log x)^2}dx

 Solution  : \int_{1}^{2}\frac{1}{x(1+\log x)^2}dx

put 1+\log x =t \Rightarrow \frac{ 1}{x}dx=dt \Rightarrow dx=x \; dt
when x=1 then t=1 when x=2 then t=1+log2
 

\begin{aligned} &\int_{1}^{2} \frac{1}{x(1+\log x)^{2}} d x=\int_{1}^{1+\log 2} \frac{1}{x \cdot t^{2}} x d t \\ &=\int_{1}^{1+\log 2} \frac{1}{t^{2}} d t \\ &=\int_{1}^{1+\log 2} t^{-2} d t \end{aligned}

\begin{aligned} &=\left[\frac{t^{-2+1}}{-2+1}\right]_{1}^{1+\log 2} \\ &=\left[\frac{t^{-1}}{-1}\right]_{1}^{1+\log 2} \\ &=-\left[\frac{1}{t}\right]_{1}^{1+\log 2} \\ &=-\left[\frac{1}{1+\log 2}-\frac{1}{1}\right] \\ &=1-\frac{1}{1+\log 2} \\ &=\frac{1+\log 2-1}{1+\log 2} \\ &=\frac{\log 2}{1+\log 2} \end{aligned}

 

Posted by

infoexpert24

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Class 12 Compartment Result 2026 LIVE: 12th supplementary marksheet out at results.digilocker.gov.in
anam-khan

CBSE Class 12 supplementary results 2026 out; 53.08% students pass
anam-khan

CBSE Class 12 Supplementary Exam 2026: 'Chapter-wise weightage ignored,' allege students; seek grace marks

Latest Question