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 R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise 18.25 Question 52 Maths Textbook Solution.

Provide Solution For  R.D.Sharma Maths Class 12 Chapter 18  Indefinite Integrals Exercise 18.25 Question 52 Maths Textbook Solution.

Answers (1)

Answer: -\sqrt{1-x^{2}}\sin ^{-1}x+x+c

Hint: Put \sin ^{-1}x=t

Given: \int \frac{x\sin ^{-1}x}{\sqrt{1-x^{2}}}dx

Solution:By letting \sin ^{-1}x=t\Rightarrow x=\sin t\Rightarrow dx=\cos tdt

               \begin{aligned} \therefore \int \frac{x \sin ^{-1} x}{\sqrt{1-x^{2}}} d x &=\int \frac{\sin t . t}{\sqrt{1-\sin ^{2} t}} \cos t d t \\ &=\int \frac{t \sin t \cos t}{\cos t} d t \\ &=\int t \sin t d t \Rightarrow t(-\cos t)-\int 1(-\cos t) d t \end{aligned}

Applying by parts

                                                 =t\cos t+\sin t+c

                                                  =t\sqrt{1-t}+\sin t+c

                                                   =\sqrt{1-x^{2}}\sin ^{-1}x+x+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 12th Result 2026 LIVE: Class 12 scores soon at cbse.gov.in, how to check, digilocker link, exam pattern
anam-khan

CBSE 12th Result 2026 Date LIVE: Class 12 marksheet on cbse.gov.in, DigiLocker soon; OSM system, passing marks
anam-khan

CBSE 12th Result 2026 Date LIVE: Class 12 results at cbse.gov.in soon; how to check on Digilocker, Umang

Latest Question