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 Indefinite Integrals Exercise 18.17 Question 8 Maths Textbook Solution

Please Solve RD Sharma Class 12 Chapter Indefinite Integrals Exercise 18.17 Question 8 Maths Textbook Solution

Answers (1)

best_answer

Answer:- \sin^{-1}\left ( \frac{x+3}{4} \right )+c

Hint: - To solve this problem, use special integration formula

Given:- \int \frac{1}{\sqrt{7-6x-x^{2}}}dx

Solution:-

Let I=\int \frac{1}{\sqrt{7-6x-x^{2}}}dx\Rightarrow \int \frac{1}{\sqrt{-\left \{ x^{2}+6x -7\right \}}}dx 

        \begin{aligned} &=\int \frac{1}{\sqrt{-\left\{x^{2}+2 x \cdot 3+(3)^{2}-(3)^{2}-7\right\}}} d x \\ &=\int \frac{1}{\sqrt{-\left\{(x+3)^{2}-9-7\right\}}} d x \Rightarrow \int \frac{1}{\sqrt{-\left\{(x+3)^{2}-16\right\}}} d x \\ &=\int \frac{1}{\sqrt{16-(x+3)^{2}}} d x \Rightarrow \int \frac{1}{\sqrt{(4)^{2}-(x+3)^{2}}} d x \\ &\text { put } \mathrm{x}+3=\mathrm{t} \Rightarrow \mathrm{dx}=\mathrm{dt} \text { then } \end{aligned}

        \begin{aligned} &I=\int \frac{1}{\sqrt{(4)^{2}-t^{2}}} d t=\sin ^{-1}\left(\frac{t}{4}\right)+c \quad\quad\quad\quad\quad\left[\because \int \frac{1}{a^{2}-x^{2}} d x=\sin ^{-1}\left(\frac{x}{a}\right)+c\right] \\ &=\sin ^{-1}\left(\frac{x+3}{4}\right)+c \quad\quad\quad\quad\quad\quad\quad\quad\quad[\because t=x+3] \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

Supreme Court to hear plea against CBSE evaluation policy for Gulf Class 12 students on July 14
anam-khan

'Award grace marks': CBSE's July 28 supplementary exam sparks student outrage over college admissions
anam-khan

CBSE Class 12 supplementary exam 2026 on July 28; LOC submission starts

Latest Question