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 30 maths textbook solution

Answers (1)


Answer: \frac{1}{2} \log \left(\frac{17}{5}\right)

Hint: you must know the rule of integration

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

Solution:  Put x^{2}+1=t

                        \begin{aligned} &2 x \; d x=d t \\\\ &x \; d x=\frac{d t}{2} \end{aligned}

        \begin{aligned} &\mathrm{I}=\frac{1}{2} \int_{2}^{4} \frac{d t}{t} \\\\ &=\frac{1}{2}[\log |t|]_{2}^{4} \end{aligned}

        \begin{aligned} &=\frac{1}{2}\left[\log \left|x^{2}+1\right|\right]_{2}^{4} \\\\ &=\frac{1}{2}[\log (16+1)+\log (4+1)] \\\\ &=\frac{1}{2} \log \left(\frac{17}{5}\right) \end{aligned}


Posted by


View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support