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 Very short answer type question 4 maths

Explain solution RD Sharma class 12 chapter 19 Definite Integrals exercise Very short answer type question 4 maths

Answers (1)

Answer: \frac{\pi }{2}

Hint: You must know the integration rules of trigonometric function with its limits

Given: \int_{\frac{-\pi}{2}}^{\frac{\pi}{2}} \cos ^{2} x \; d x

Solution: \int_{\frac{-\pi}{2}}^{\frac{\pi}{2}} \cos ^{2} x \; d x

\begin{aligned} &=\int_{\frac{-\pi}{2}}^{\frac{\pi}{2}} \frac{1+\cos 2 x}{2} d x \\\\ &=\frac{1}{2} \int_{\frac{-\pi}{2}}^{\frac{\pi}{2}} 1 . d x+\frac{1}{2} \int_{\frac{-\pi}{2}}^{\frac{\pi}{2}} \cos 2 x\; d x \end{aligned}

\begin{aligned} &=\frac{1}{2}[x]_{\frac{-\pi}{2}}^{\frac{\pi}{2}}+\frac{1}{2}\left[\frac{\sin 2 x}{2}\right]_{\frac{\pi}{2}}^{\frac{\pi}{2}} \\\\ &=\frac{1}{2}\left[\frac{\pi}{2}-\left(-\frac{\pi}{2}\right)\right]+\frac{1}{4}\left[\sin \frac{2(\pi)}{2}+\sin \frac{2(-\pi)}{2}\right] \end{aligned}

\begin{aligned} &=\frac{1}{2}\left[\frac{2 \pi}{2}\right]+\frac{1}{4}[0+0] \\\\ &=\frac{\pi}{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

Similar Questions

Trending Articles/News

anam-khan

CBSE question papers QR codes part of 'internal systems'; board cautions 'unverified claims'
anam-khan

Delhi court grants interim bail to Class 12 student in stabbing case to appear for CBSE exam
anam-khan

CBSE Class 12 History Exam 2026 Analysis: Moderate paper, tricky MCQs, student-friendly pattern

Latest Question