Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Explain solution RD Sharma class 12 Chapter 18 Indefinite Integrals exercise 18.28 question 15

Explain solution RD Sharma class 12 Chapter 18 Indefinite Integrals exercise 18.28 question 15

Answers (1)

best_answer

Answer:-

\frac{1}{2}(x-a) \sqrt{2 a x-x^{2}}+\frac{a^{2}}{2} \sin ^{-1}\left(\frac{x-a}{a}\right)+c

Hint:-

Using the formula

\begin{aligned} &\int \sqrt{a^{2}-x^{2}}=\frac{1}{2} x \sqrt{a^{2}-x^{2}}+\frac{a^{2}}{2} \sin ^{-1}\left(\frac{x}{a}\right)+c \\\\ &\int \sqrt{x^{2}-a^{2}} d x=\frac{x}{2} \sqrt{x^{2}-a^{2}}-\frac{a^{2}}{2} \log \left|x+\sqrt{x^{2}-a^{2}}\right|+c \\\\ &\int \sqrt{x^{2}+a^{2}} d x=\frac{x}{2} \sqrt{x^{2}+a^{2}}+\frac{a^{2}}{2} \log \left|x+\sqrt{x^{2}+a^{2}}\right|+c \end{aligned}

 

Given:-

 

\int \sqrt{2 a x-x^{2}} d x

Solution:-

Let,

\begin{aligned} & I=\int \sqrt{2 a x-x^{2}} d x \\ &\therefore I=\int \sqrt{-\left(x^{2}-2 a x\right)} d x=\int \sqrt{(a)^{2}-\left(x^{2}-2 a x+a^{2}\right)} d x \end{aligned}

We have

I=\int \sqrt{(a)^{2}-(x-a)^{2}} d x

As I match with the form

\begin{aligned} &\int \sqrt{a^{2}-x^{2}}=\frac{1}{2} x \sqrt{a^{2}-x^{2}}+\frac{a^{2}}{2} \sin ^{-1}\left(\frac{x}{a}\right)+c \\\\ &I=\frac{x-a}{2} \sqrt{a^{2}-(x-a)^{2}}+\frac{a^{2}}{2} \sin ^{-1}\left(\frac{x-a}{a}\right)+c \\\\ &I=\frac{1}{2}(x-a) \sqrt{2 a x-x^{2}}+\frac{a^{2}}{2} \sin ^{-1}\left(\frac{x-a}{a}\right)+c \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

CBSE announces deadline for Class 10, 12 direct admissions, subject change
anam-khan

CBSE warns about unauthorised sources offering ‘quick’ ways of getting duplicate marksheets, certificates
anam-khan

CBSE unveils 8 major changes for Class 10, 12 board exams; what students need to know

Latest Question