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 18.9 question 9 maths textbook solution

Please solve RD Sharma class 12 chapter Indefinite Integrals exercise 18.9 question 9 maths textbook solution

Answers (1)

Answer: 2 \sqrt{x-\cos x}+c

Hint: Use substitution method to solve this integral.

Given: \int \frac{1+\sin x}{\sqrt{x-\cos x}} d x

Solution:

        \text { Let } I=\int \frac{1+\sin x}{\sqrt{x-\cos x}} d x

        \begin{aligned} &\text { Put } x-\cos x=t \Rightarrow(1+\sin x) d x=d t \\ &\Rightarrow(1+\sin x) d x=d t \text { then } \end{aligned}

        \begin{aligned} I &=\int \frac{1}{\sqrt{t}} d t=\int t^{\frac{-1}{2}} d t \\ &=\frac{t^{\frac{-1}{2}+1}}{\frac{-1}{2}+1}+c=\frac{t^{\frac{1}{2}}}{\frac{1}{2}}+\mathrm{c} \quad\left[\because \int x^{n} d x=\frac{x^{n+1}}{n+1}+c\right] \end{aligned}

            =2 \sqrt{t}+c

            =2 \sqrt{x-\cos x}+c\; \; \; \; \; [\because t=x-\cos x]

Posted by

infoexpert26

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