Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Evaluate the definite integrals in Exercises 1 to 20. Integral 0 to pi sin^2 x/2 - cos^2 x/\2 dx

Evaluate the definite integrals in Exercises 1 to 20.

    Q18.    \int^\pi_0(\sin^2\frac{x}{2} - \cos^2\frac{x}{2})dx

Answers (1)

best_answer

Given integral: \int^\pi_0(\sin^2\frac{x}{2} - \cos^2\frac{x}{2})dx

Consider the integral \int (\sin^2\frac{x}{2} - \cos^2\frac{x}{2})dx

can be rewritten as: -\int (\cos^2\frac{x}{2} - \sin^2\frac{x}{2})dx = -\int_0^{\pi} \cos x dx

                                                                                    = \sin x

So, we have the function of x, f(x) =\sin x

Now, by Second fundamental theorem of calculus, we have

I = f(\pi) - f(0)

\Rightarrow \sin \pi - \sin 0 = 0-0 =0

Posted by

Divya Prakash Singh

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 board exams 2025 to have 50% competency-based questions; no change in 10th
anam-khan

CBSE Class 12 board exams 2024 over; expected result date, trends of last 10 years

Latest Question