Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Provide solution for RD Sharma maths class 12 chapter 19 Definite Integrals exercise Multiple choice question 39

Provide solution for RD Sharma maths class 12 chapter 19 Definite Integrals exercise Multiple choice question 39

Answers (1)

Answer:

I=\frac{a+b}{2} \int_{a}^{b} f(x) d x

Hint:

To solve this we will split (a+b-x)

Given:

\int(a+b-x)=f(x)

Solution:

\int(a+b-x)=f(x)

Let

\begin{aligned} &I=\int_{a}^{b} x \cdot f(x) d x \ldots(i) \\\\ &\int_{a}^{b} f(x) d x=\int_{a}^{b}(a+b-x) d x \end{aligned}

\begin{aligned} &I=\int_{a}^{b}(a+b-x) \cdot f(a+b-x) d x \\\\ &I=\int_{a}^{b}(a+b-x) \cdot f(x) d x \end{aligned}

I=\int_{a}^{b}(a+b) \cdot f(x) d x-\int_{a}^{b} x f(x) d x \ldots(i i)

Adding equation (i) and (ii)

I+I=\int_{a}^{b} x f(x) d x+\int_{a}^{b}(a+b) \cdot f(x) d x-\int_{a}^{b} x f(x) d x

\begin{aligned} &2 I=\int_{a}^{b}(a+b) f(x) d x \\\\ &I=\frac{1}{2} \int_{a}^{b}(a+b) f(x) d x \\\\ &I=\frac{a+b}{2} \int_{a}^{b}(a+b) f(x) d x \end{aligned}

 

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

CBSE Date Sheet 2027 LIVE: Class 10, 12 timetable soon; official website, exam mode, guidelines
anam-khan

Board Exams 2027: CBSE 10th, 12th sample papers, marking scheme out at cbseacademic.nic.in, direct link
anam-khan

CBSE Board Exam Dates 2027 LIVE: CBSE Class 10, 12 sample papers out, time table soon

Latest Question