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 7

Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise 18.14 Question 7

Answers (1)

best_answer

Answer: \frac{1}{b} \sin ^{-1}\left(\frac{b x}{a}\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

\begin{aligned} &\text { Put } b x=t \Rightarrow b d x=d t \Rightarrow d x=\frac{d t}{b} \text { then } \\ &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 \end{aligned}

\begin{aligned} &=\frac{1}{b} \sin ^{-1}\left(\frac{t}{a}\right)+c \quad\left[\because \int \frac{1}{\sqrt{a^{2}-x^{2}}} d x=\sin ^{-1}\left(\frac{x}{a}\right)+c\right] \\\\ &=\frac{1}{b} \sin ^{-1}\left(\frac{b x}{a}\right)+c \quad[\because t=b x] \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

NSUI stages protest outside CBSE headquarters, demands rollback of OSM
anam-khan

CBSE revaluation payment system faces malicious attack; IIT experts, PSU banks step in
anam-khan

From next year, CBSE Class 12 answer sheets on Digilocker: Education ministry

Latest Question