Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

Provide Solution For R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise Revision Exercise Question 42 Maths Textbook Solution.

Answers (1)

Answer:

$\ln \left|x+\sqrt{x^{2}-a^{2}}\right|+C^{\prime}$

$\text { where } C^{\prime}=C-\ln a$

Given:

$\int \frac{1}{\sqrt{x^{2}-a^{2}}} d x$

Hint:

In this statement we have to assume x as asecθ.

Solution:

$I=\int \frac{1}{\sqrt{x^{2}-a^{2}}} d x$

$\text { putting } x=a \sec \theta$

$\Rightarrow d x=a \sec \theta \tan \theta d \theta$

$I=\int \frac{a \sec \theta \tan \theta d \theta}{\sqrt{a^{2} \sec ^{2} \theta-a^{2}}}$

$=\int \frac{a \sec \theta \tan \theta d \theta}{a \cdot \tan \theta}$

$=\int \sec \theta \tan \theta d \theta$

$=\ln |\sec \theta+\tan \theta|+C$

$=\ln \left|\sec \theta+\sqrt{\sec ^{2} \theta-1}\right|+C$

$=\ln \left|\frac{x}{a}+\sqrt{\left(\frac{x}{a}\right)^{2}}-1\right|+C$

$=\ln \left|\frac{x+\sqrt{x^{2}-a^{2}}}{a}\right|+C$

$=\ln \left|x+\sqrt{x^{2}-a^{2}}\right|+C$

$=\ln \left|x+\sqrt{x^{2}-a^{2}}\right|-\ln a+C$

$=\ln \left|x+\sqrt{x^{2}-a^{2}}\right|+C^{\prime}$

$\text { where } C^{\prime}=C-\ln a$

Posted by

infoexpert21

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

Board Exam Time Table 2025 Live: UP Board exams from February 24; CBSE, BSEB date sheet soon

anam-khan

CBSE Date Sheet 2025 Live: Class 10, 12 board exam dates soon; syllabus, sample papers

anam-khan

Extra time in CBSE exams for students with type 1 diabetes: Kerala SHRC seeks report on plea

Latest Question