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 Date Sheet 2025: When to expect Class 10, 12 board exam time table?
anam-khan

CBSE introduces CCTV policy in board exams 2025; schools fixed as centres must have facility
anam-khan

CBSE gives parents, schools till October 16 to register students in Classes 9, 11

Latest Question