Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Provide solution for RD Sharma maths class 12 chapter 19 Definite Integrals exercise Very short answer type question 2

Provide solution for RD Sharma maths class 12 chapter 19 Definite Integrals exercise Very short answer type question 2

Answers (1)

Answer: \frac{\pi }{4}

Hint: You must know the integration rule of trigonometric functions.

Given: \int_{0}^{\frac{\pi}{2}} \cos ^{2} x \; d x

Solution:  \int_{0}^{\frac{\pi}{2}} \cos ^{2} x \; d x

\begin{aligned} &=\int_{0}^{\frac{\pi}{2}} \frac{1+\cos 2 x}{2} d x \\\\ &=\frac{1}{2} \int_{0}^{\frac{\pi}{2}} 1 . d x+\frac{1}{2} \int_{0}^{\frac{\pi}{2}} \cos 2 x \; d x \end{aligned}

\begin{aligned} &=\frac{1}{2}[x]_{0}^{\frac{\pi}{2}}+\frac{1}{2}\left[\frac{\sin 2 x}{2}\right]_{0}^{\frac{\pi}{2}} \\\\ &=\frac{1}{2}\left[\frac{\pi}{2}-0\right]+\frac{1}{4}\left[\sin \frac{2 \pi}{2}-\sin 0\right] \\\\ &=\frac{\pi}{4} \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

PM Modi's Pariksha Pe Charcha 2025 to be held next month, registrations open till January 14
anam-khan

CBSE Board Exams 2025: Online portal for availing exemptions by CWSN students opens
anam-khan

Board Exams: States agree to equivalence; no question paper ‘jumbling’ from next year, says PARAKH CEO

Latest Question