Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Need Solution for R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise Revision Exercise Question 48 Maths Textbook Solution.

Need Solution for R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise Revision Exercise Question 48 Maths Textbook Solution.

Answers (1)

Answer:

I=-\ln \left|(\cos x-1)+\sqrt{\cos ^{2} x-2 \cos x+3}\right|+c

Given:

\int \frac{\sin x}{\sqrt{\cos ^{2} x-2 \cos x-3}} d x

Hint:

To solve this statement we have to use standard formula.

Solution: 

I=\int \frac{\sin x}{\sqrt{\cos ^{2} x-2 \cos x-3}} d x                                [\because \cos x=t, d t=-\sin x d x=>\sin x d x=-d t]

    I=-\int \frac{d t}{\sqrt{t^{2}-2 t-3}}

I=-\int \frac{d t}{\sqrt{(t-1)^{2}-1-3}}

 

I=-\int \frac{d t}{\sqrt{(t-1)^{2}-4}}

I=-\int \frac{d t}{\sqrt{(t-1)^{2}-(2)^{2}}}                                    \left[\because \int \frac{d x}{\sqrt{x^{2}-a^{2}}}=\ln \left|x+\sqrt{x^{2}-a^{2}}\right|+c\right.

I=-\ln \mid(t-1)+\sqrt{(t-1)^{2}-(2)^{2} \mid+} c

I=-\ln \left|(t-1)+\sqrt{t^{2}-2 t-3}\right|+c

I=-\ln \left|(\cos x-1)+\sqrt{\cos ^{2} x-2 \cos x+3}\right|+c

 

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

CBSE, JKBOSE, Assam board exams today; timings, passing marks, key guidelines
anam-khan

CBSE bans use of ChatGPT, mobile during board exam 2025; warns students of action for spreading rumors
anam-khan

Delhi metro to prioritise CBSE Class 10, 12 students for frisking, ticketing during board exam 2025

Latest Question