Get Answers to all your Questions

header-bg qa

Please solve RD Sharma class 12 chapter 19 Definite Integrals exercise Multiple choice question 21 maths textbook solution

Answers (1)

best_answer

Answer:

\frac{1}{2}

Given:

\int_{0}^{a} \frac{1}{1+4 x^{2}} d x=\frac{\pi}{8}

Hint:

To solve this equation, we will do 4x in whole system.
 

Explanation:  

Let

\begin{aligned} &I=\int_{0}^{a} \frac{1}{1+4 x^{2}} d x \\\\ &I=\int_{0}^{a} \frac{1}{1+(2 x)^{2}} d x \end{aligned}

\begin{aligned} &=\left[\frac{1}{2} \tan ^{-1}\left(\frac{2 x}{1}\right)\right]_{0}^{a} \\\\ &=\frac{\pi}{8} \\\\ &\frac{1}{2}\left[\tan ^{-1}(2 a)-\tan ^{-1}(0)\right]=\frac{\pi}{8} \end{aligned}

\begin{aligned} &\frac{1}{2}\left[\tan ^{-1}(2 a)\right]=\frac{\pi}{8} \\\\ &\tan ^{-1}(2 a)=\frac{\pi}{4} \end{aligned}

\begin{aligned} &2 a=\tan \frac{\pi}{4} \\\\ &2 a=1 \\\\ &a=\frac{1}{2} \end{aligned}

Posted by

infoexpert26

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads