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 19.4 (a) Question 6 textbook solution.

Provide solution for  RD Sharma maths Class 12 Chapter 19 Definite Integrals Exercise 19.4 (a) Question 6 textbook solution.

Answers (1)

Answer : a

Given : \int_{-a}^{a} \frac{1}{1+a^{x}} d x, a>0

Hint : Use the formula of \int_{-a}^{a} f(x) d x=2 \int_{0}^{a} f(x) d x

Solution : I=\int_{-a}^{a} \frac{1}{1+a^{x}} d x \quad-----(1)

We know that \int_{a}^{b} f(x) d x=\int_{a}^{b} f(a+b-x) d x

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

Add (1) and (2)

\begin{aligned} 2 I &=\int_{-a}^{a} \frac{1+a^{x}}{a^{x}+1} d x \\ 2 I &=\int_{-a}^{a} 1 . d x \end{aligned}

\begin{aligned} &2 I=(x)_{-a}^{a} \\ &2 I=2 a \\ &I=a \end{aligned}

Posted by

infoexpert23

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 Class 12 result verification 2024 application out at cbse.gov.in; last date, fees
anam-khan

CBSE results 2024 later for 102 students over fake certificates; board issues show cause notice
anam-khan

What after CBSE Class 12 results 2024? From CUET UG to JEE Advanced, all you need to know

Latest Question