Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Need Solution for R.D.Sharma Maths Class 12 Chapter 19 definite Integrals Exercise 19.1 Question 17 Maths Textbook Solution.

Need Solution for R.D.Sharma Maths Class 12 Chapter 19 definite Integrals Exercise 19.1 Question 17 Maths Textbook Solution.

Answers (1)

Answer:\frac{\pi }{4}

Hint: Use indefinite formula then put the limit to solve this integral

Given: \int_{0}^{\frac{\pi }{2}}\cos ^{2}xdx

Solution:\int_{0}^{\frac{\pi }{2}}\cos ^{2}xdx

=\int_{0}^{\frac{\pi}{2}}\left(\frac{1+\cos 2 x}{2}\right) d x \quad\left[\begin{array}{l} 2 \cos ^{2} \theta=1+\cos 2 \theta \\ \cos ^{2} \theta=\frac{1+\cos 2 \theta}{2} \end{array}\right]

\begin{aligned} &=\int_{0}^{\frac{\pi}{2}}\left(\frac{1}{2}+\frac{\cos 2 x}{2}\right) d x=\int_{0}^{\frac{\pi}{2}} \frac{1}{2} d x+\frac{1}{2} \int_{0}^{\frac{\pi}{2}} \cos 2 x d x \\ &=\frac{1}{2} \int_{0}^{\frac{\pi}{2}} x^{0} d x+\frac{1}{2} \int_{0}^{\frac{\pi}{2}} \cos 2 x d x \end{aligned} \quad\left[\begin{array}{l} \int x^{n} d x=\frac{x^{n+1}}{n+1} \\ \int \cos a x d x=\frac{\sin a x}{a} \end{array}\right]

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

=\frac{\pi }{4}+\frac{1}{4}\left [ \sin \pi -\sin 0 \right ]

=\frac{\pi }{4}

Posted by

infoexpert21

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 Paper Analysis: Students find exam easy, well-balanced; mostly previous year questions
anam-khan

CBSE Class 12: Delhi Government school teachers ask board to put on-screen marking system on hold
anam-khan

CBSE Board Exam 2026 LIVE: CBSE Class 12 Chemistry question paper analysis; answer key

Latest Question