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 6

Provide solution for RD Sharma maths class 12 chapter 19 Definite Integrals exercise Very short answer type question 6

Answers (1)

Answer: 0

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


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

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

\begin{aligned} &f(x)=x \cos ^{2} x \\\\ &f(-x)=(-x) \cos ^{2}(-x) \\\\ &=-x \cos ^{2} x \\\\ &=-f(x) \end{aligned}

Hence, f(x) is an odd function.

Since,\int_{-a}^{a} f(x) d x=0    if f(x) is an odd

\therefore \int_{\frac{-\pi}{2}}^{\frac{\pi}{2}} x \cos ^{2} x\; d x=0

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