Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Explain solution RD Sharma class 12 chapter 19 Definite Integrals exercise Multiple choice question 41 maths

Explain solution RD Sharma class 12 chapter 19 Definite Integrals exercise Multiple choice question 41 maths

Answers (1)

Answer:

I=0

Hint:

To solve this equation we use \int_{0}^{a} f(x) d x   formula.

Given:

\int_{0}^{\frac{\pi}{2}} \log \left[\frac{4+3 \sin x}{4+3 \cos x}\right] d x

Solution:

Let

\begin{aligned} &I=\int_{0}^{\frac{\pi}{2}} \log \left[\frac{4+3 \sin x}{4+3 \cos x}\right] d x \ldots(i) \\\\ &\int_{0}^{a} f(x) d x=\int_{0}^{a}(a-x) d x \end{aligned}

\begin{aligned} &I=\int_{0}^{\frac{\pi}{2}} \log \left[\frac{4+3 \sin \left(\frac{\pi}{2}-x\right)}{4+3 \cos \left(\frac{\pi}{2}-x\right)}\right] d x \\\\ &I=\int_{0}^{\frac{\pi}{2}} \log \left[\frac{4+3 \cos x}{4+3 \sin x}\right] d x \ldots(i i) \end{aligned}

Adding (i) and (ii)

\begin{aligned} &2 I=\int_{0}^{\frac{\pi}{2}}\left(\log \left[\frac{4+3 \cos x}{4+3 \sin x}\right]+\log \left[\frac{4+3 \sin x}{4+3 \cos x}\right]\right) d x \\\\ &2 I=\int_{0}^{\frac{\pi}{2}}\left(\log \left[\frac{4+3 \cos x}{4+3 \sin x}\right] \cdot \log \left[\frac{4+3 \sin x}{4+3 \cos x}\right]\right) d x \end{aligned}

\begin{aligned} &2 I=\int_{0}^{\frac{\pi}{2}} 1 d x \\\\ &2 I=0 \\\\ &I=0 \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

Similar Questions

Trending Articles/News

anam-khan

CBSE practical exams 2026 will be cancelled over non-compliance with guidelines, says board

Latest Question