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 6

Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise 18.14 Question 6

Answers (1)

best_answer

Answer:  \frac{1}{b} \log \left|b x+\sqrt{a^{2}+b^{2} x^{2}}\right|+c

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

Given:  \int \frac{1}{\sqrt{a^{2}+b^{2} x^{2}}} d x

Solution:

Let  I=\int \frac{1}{\sqrt{a^{2}+b^{2} x^{2}}} d x

\text { Put } b x=t \Rightarrow b d x=d t \Rightarrow d x=\frac{d t}{b} \text { then }

\begin{aligned} &I=\int \frac{1}{\sqrt{a^{2}+t^{2}}} \frac{d t}{b}=\frac{1}{b} \int \frac{1}{\sqrt{a^{2}+t^{2}}} d t \\\\ &=\frac{1}{b} \log \left|t+\sqrt{a^{2}+t^{2}}\right|+c \quad\quad\quad\quad\quad\quad\quad\left[\because \int \frac{1}{\sqrt{x^{2}+a^{2}}} d x=\log \left|x+\sqrt{x^{2}+a^{2}}\right|+c\right] \end{aligned}

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

 

 

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 12th result 2025 sees more in compartment, JNVs on top, perfect-scorers in minor subjects
anam-khan

Low score in CBSE results? Courses, career options after 12th open to you
anam-khan

CBSE class 10, 12 results: West Bengal CM Mamata Banerjee congratulates successful candidates

Latest Question