Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Please Solve RD Sharma Class 12 Chapter 18 Indefinite Integrals Exercise 18.28 Question 5 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 18 Indefinite Integrals Exercise 18.28 Question 5 Maths Textbook Solution.

Answers (1)

best_answer

Answer:-

\frac{1}{2} \sin x \sqrt{4-\sin ^{2} x}+2 \sin ^{-1} \frac{\sin x}{2}+c

Hint:-

Taking \sin x = t

Given:-

\int \cos x \sqrt{4-\sin ^{2} x} d x

Solution:-

By taking \sin x = t

\cos x d x=d t

Hence

\begin{aligned} &=\int \sqrt{4-t^{2}} d t \\\\ &=\int \sqrt{(2)^{2}-(t)^{2}} d t \\\\ &=\frac{1}{2} t \sqrt{4-t^{2}}+\frac{1}{2}(2)^{2} \sin ^{-1} \frac{t}{2}+c \end{aligned}

 

Using the formula

\begin{aligned} &\int \sqrt{a^{2}-x^{2}}=\frac{1}{2} x \sqrt{a^{2}-x^{2}}+\frac{a^{2}}{2} \sin ^{-1} \frac{x}{a}+c \\\\ &=\frac{1}{2} \sin x \sqrt{4-\sin ^{2} x}+2 \sin ^{-1} \frac{\sin x}{2}+c \end{aligned}

 

 

 

 

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

CBSE Supplementary Result 2025 LIVE: Class 10, 12 compartment result soon on results.cbse.nic.in; updates
anam-khan

CBSE Supplementary Result 2025 LIVE: Class 10, 12 supplementary result soon on results.cbse.nic.in
anam-khan

CBSE Class 12 revaluation, verification results 2025 out at results.cbse.nic.in

Latest Question