Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • By using the properties of definite integrals, evaluate the integrals in Exercises 1 to 19. 14.

By using the properties of definite integrals, evaluate the integrals in Exercises 1 to 19.

    Q14.    \int_0^{2\pi}\cos^5xdx

Answers (1)

best_answer

We have                      I\ =\ \int_0^{2\pi}\cos^5xdx

It is known that :-

                                    \int_0^{2a}f(x)dx\ =\ 2\int_0^{a}f(x)dx                                           If   f (2a - x) = f(x)

                                                                =\ 0                                                                   If  f (2a - x) =  -  f(x) 

Now,    using the above property                        

                                           \cos^5(\Pi - x)\ =\ - \cos^5x

Therefore,                        I\ =\ 0

Posted by

Devendra Khairwa

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 Class 12 Chemistry Exam Analysis 2025: Paper 'moderately difficult' but well balanced
anam-khan

CBSE Class 12 board exam still once a year; 20 lakh expected to appear in 2026 from February 17
anam-khan

CBSE board exams twice a year from 2025-26; 2 subject groups, 'better of two marks' in draft policy

Latest Question