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 Class 12 Chapter 19 Definite Integrals Exercise Revision Exercise Question 57

Provide Solution for RD Sharma Class 12 Chapter 19 Definite Integrals Exercise Revision Exercise Question 57

Answers (1)

best_answer

Answer:  \frac{\pi}{\sqrt{35}}

Hint: To solve this equation, we convert cos x into tan x

Given:  \int_{0}^{\pi} \frac{d x}{6-\cos x}

Solution

I= \int _{0}^{\pi}\frac{dx}{6-\left ( \frac{1-\tan ^{2}\frac{x}{2}}{1+\tan\frac{x}{2}} \right )}

=\int_{0}^{\pi} \frac{\sec ^{2} \frac{x}{2}}{6+6 \tan ^{2} \frac{x}{2}-1+\tan ^{2} \frac{x}{2}} d x

\begin{aligned} &=\frac{1}{7} \int_{0}^{\pi} \frac{\sec ^{2} \frac{x}{2}}{\frac{5}{7}+\tan ^{2} \frac{x}{2}} d x \\ & \end{aligned}

\text { Let } \tan \frac{x}{2}=t \\

\frac{1}{2} \sec ^{2} \frac{x}{2} d x=d t

\begin{aligned} &\sec ^{2} \frac{x}{2} d x=2 d t \\ & \end{aligned}

I=\frac{2}{7} \int_{0}^{\pi} \frac{d t}{\sqrt{\frac{5}{7}}^{2}+t^{2}}

\begin{aligned} &I=\frac{2}{7} \frac{1}{\sqrt{\frac{5}{7}}}\left(\tan ^{-1} \frac{t}{\sqrt{\frac{5}{7}}}\right)_{0}^{\infty} \\ & \end{aligned}

=\frac{2}{\sqrt{35}}\left(\frac{\pi}{2}-0\right) \\

I=\frac{\pi}{\sqrt{35}}

Posted by

infoexpert27

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

CIC asks CBSE to disclose tender process for exam answer sheet procurement under RTI Act
anam-khan

CBSE 10th Second Board Result 2026 LIVE: Class 10 session 2 scores soon at cbse.gov.in; passing marks
anam-khan

Delhi HC refuses to direct reopening of CBSE class 12 re-evaluation portal

Latest Question