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

Looking forward to interacting with students at Pariksha Pe Charcha 2026: PM Narendra Modi
anam-khan

CBSE Exam Dates 2026 LIVE: CBSE Class 10th, 12th revised date sheet at cbse.gov.in; how to download, updates
anam-khan

CBSE board exam 2026 scheduled on March 3 postponed for Class 10, 12; revised date sheet out

Latest Question