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 18.28 Question 1

Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise 18.28 Question 1

Answers (1)

Answer:-

\frac{1}{2}(x-1) \sqrt{3+2 x-x^{2}}+2 \sin ^{-1}\left(\frac{x-1}{2}\right)+c

Hint:-

Adding and subtracting with 1.

Given:-

\int \sqrt{3+2 x-x^{2}} d x

Solution:-

\begin{aligned} &=\int \sqrt{4+2 x-x^{2}-1} d x \\\\ &=\int \sqrt{(2)^{2}-\left(x^{2}-2 x+1\right)} d x \\\\ &=\int \sqrt{(2)^{2}-(x-1)^{2}} d x \end{aligned}

\begin{aligned} &=\frac{1}{2}(x-1) \sqrt{3+2 x-x^{2}}+\frac{1}{2} \times(2)^{2} \sin ^{-1}\left(\frac{x-1}{2}\right)+c \\\\ &=\frac{1}{2}(x-1) \sqrt{3+2 x-x^{2}}+2 \sin ^{-1}\left(\frac{x-1}{2}\right)+c \end{aligned}

 

Using the formula

 

\int \sqrt{a^{2}+x^{2}} d x=\frac{1}{2} x \sqrt{a^{2}+x^{2}}+\frac{1}{2} a^{2} \sin ^{-1}\left(\frac{x}{2}\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

Board Exam Time Table 2025 Live: UP Board exams from February 24; CBSE, BSEB date sheet soon
anam-khan

CBSE Date Sheet 2025 Live: Class 10, 12 board exam dates soon; syllabus, sample papers
anam-khan

Extra time in CBSE exams for students with type 1 diabetes: Kerala SHRC seeks report on plea

Latest Question