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 class12 Chapter Definite Integrals exercise 19.2 question 9.

Provide solution for RD Sharma maths class12 Chapter Definite Integrals exercise 19.2 question 9.

Answers (1)

\frac{\pi}{4}

Hint: We use indefinite integral formula then put limits to solve this integral.

Given: \int_{0}^{1}\frac{2x}{1+x^4}dx

Solution: I=\int_{0}^{1}\frac{2x}{1+x^4}dx

Put x^2=t

2x\; \; dx=dt

When x=0  then t=0  and

when x=1  then t=1

I=\int_{0}^{1}\frac{1}{t^2+1}dt                            \left[\int \frac{1}{1+x^{2}} d x=\tan ^{-1} \frac{x}{a}\right]

\begin{aligned} &=\left[\tan ^{-1}\left(\frac{t}{1}\right)\right]_{0}^{1} \mid \\ &=\left[\tan ^{-1} 1-\tan ^{-1} 0\right] \\ &=\frac{\pi}{4}-0=\frac{\pi}{4} \end{aligned}

Posted by

infoexpert24

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 2026 Class 12 LIVE: 12th Biology question paper with solutions, analysis soon; passing criteria
anam-khan

CBSE 12th Computer Science Analysis 2026: Competency-based, direct questions, ‘easy’ MCQs; IP paper ‘balanced’
anam-khan

CBSE Class 12 Computer Science, IT, IP Exam 2026 LIVE: Question papers 'moderate', analysis updates

Latest Question