Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Please solve RD Sharma class 12 chapter Areas of Bounded Region exercise 20.1 question 13 maths textbook solution

Please solve RD Sharma class 12 chapter Areas of Bounded Region exercise 20.1 question 13 maths textbook solution

Answers (1)

Answer:

\frac{\pi a^{2}}{4} s q \cdot \text { unit }

Hint:

y=\sqrt{a^{2}-x^{2}} \text { at line } x=0, x=a

Given: Determine the area under curve y=\sqrt{a^{2}-x^{2}} include between line x=0 and x=a

Solution:

\begin{aligned} &y=\sqrt{a^{2}-x^{2}} \\\\ &y^{2}=a^{2}-x^{2} \\\\ &x^{2}+y^{2}=a^{2} \end{aligned}

Required area =  area of shaded region

\begin{aligned} &=\int_{0}^{a} y d x \\\\ &=\int_{0}^{a} \sqrt{a^{2}-x^{2}} d x \\\\ &=\left[\frac{x}{2} \sqrt{a^{2}-x^{2}}+\frac{a^{2}}{2} \sin ^{-1} \frac{x}{a}\right]_{0}^{a} \end{aligned}

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

=\frac{\pi a^{2}}{4} s q \cdot u n i t

      

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

Delhi court grants interim bail to Class 12 student in stabbing case to appear for CBSE exam
anam-khan

CBSE Class 12 History Exam 2026 Analysis: Moderate paper, tricky MCQs, student-friendly pattern
anam-khan

CBSE 12th biology, physical education exams 2026 for sports event participants on April 11 and 13

Latest Question