Get Answers to all your Questions

header-bg qa

Please solve RD Sharma class 12 chapter 19 Definite Integrals exercise Very short answer type question 25 maths textbook solution

Answers (1)


Answer: \log _{e} 2

Hint: you must know the rule of integration for function of x

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

Solution:  \int_{0}^{1} \frac{2 x}{1+x^{2}} \mathrm{dx}

Put  1+x^{2}=t

        2 x \; d x=d t

                    \begin{aligned} &=\int_{0}^{1} \frac{d t}{t} \\\\ &=[\log t]_{0}^{1} \end{aligned}

                    \begin{aligned} &=\left[\log \left(1+x^{2}\right)\right]_{0}^{1} \\\\ &=[\log (1+1)-\log (1+0)] \\\\ &=\log _{e} 2 \end{aligned}


Posted by


View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support