Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • The value of the integral <img alt="\int_{1}^{3}\left ( \tan ^{-1}\frac{x}{x^{2}+1}+\tan ^{-1}\frac{x^{2}+1}{x} \right )" src="https://learn.careers360.com/latex-image/?%5Cint_%7B1%7D%5E%7B3%7

The value of the integral \int_{1}^{3}\left ( \tan ^{-1}\frac{x}{x^{2}+1}+\tan ^{-1}\frac{x^{2}+1}{x} \right ) dx is equal to

Option: 1

\pi


Option: 2

2\pi


Option: 3

4\pi


Option: 4

none of these


Answers (1)

best_answer

 

Constant of integration: -

\frac{\mathrm{d} }{\mathrm{d} x}\left ( F\left ( x \right )+C \right )=\frac{\mathrm{d} }{\mathrm{d} x}F \left ( x \right )+0=f\left ( x \right )

Hence    \int f\left ( x \right )dx=F\left ( x \right )+C

- wherein

Where C is the constant of integration .

 

 

lower and upper limit -

 

\int_{a}^{b}f\left ( x \right )dx= \left ( F\left ( x \right ) \right )_{a}^{b}

                = F\left ( b \right )-F\left ( a \right )

 

- wherein

Where a is lower and b is upper limit.

 

\\\tan^{-1} \left(\frac{1}{x}\right)=\cot^{-1} \left(x\right)\\\\tan^{-1} x+\cot^{-1}x=\frac{\pi}{2}

I= \int_{1}^{3}\left ( tan^{-1}\frac{x}{x^{2}+1}+tan^{-1}\frac{x^{2}+1}{x} \right )dx=\int_{1}^{3}\frac{\pi }{2}\: dx= (3-1)\: \frac{\pi}{2}=\pi

Posted by

seema garhwal

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions