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 RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise 18.14 Question 8

Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise 18.14 Question 8

Answers (1)

Answer: -\log \left|(2-x)+\sqrt{(2-x)^{2}+1}\right|+c

Hint: To solve this integral, use special integral formula.

Given:  \int \frac{1}{\sqrt{(2-x)^{2}+1}} d x

Solution:

Let

I=\int \frac{1}{\sqrt{(2-x)^{2}+1}} d x

\text { Put } 2-x=t \Rightarrow-d x=d t \Rightarrow d x=-d t \text { then }

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

=-\log \left|t+\sqrt{t^{2}+1}\right|+c \quad\quad\quad\quad\quad\quad\quad\left[\because \int \frac{1}{\sqrt{a^{2}+x^{2}}} d x=\log \left|x+\sqrt{a^{2}+x^{2}}\right|+c\right]

=-\log \left|(2-x)+\sqrt{(2-x)^{2}+1}\right|+c

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

PM Modi's Pariksha Pe Charcha 2025 to be held next month, registrations open till January 14
anam-khan

CBSE Board Exams 2025: Online portal for availing exemptions by CWSN students opens
anam-khan

Board Exams: States agree to equivalence; no question paper ‘jumbling’ from next year, says PARAKH CEO

Latest Question