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 20 Areas of Bounded Region Exercise 20.3 question 19.

Provide solution for RD Sharma Maths Class 12 Chapter 20 Areas of Bounded Region Exercise 20.3 question 19.

Answers (1)

Answer:

\frac{4a^2}{3}9(\sqrt{3}+4\pi)

Hint:

\int \sqrt{a^{2}-x^{2}} d x=\frac{x}{2} \sqrt{a^{2}-x^{2}}+\frac{a^{2}}{2} \sin -\frac{1}{a}+c \text {. } .

Given:

Given curves x^2+y^2=16a^2 and y^2=6ax .

Solution:

The point of intersection of circle

x^2+y^2=16a^2

And parabola,  y^2=6ax is

\begin{aligned} &x^{2}+6 a x-16 a^{2}=0 \\ &(x+8 a)(x-2 a)=0 \\ &x=2 a, y=\pm 2 \sqrt{3} a \end{aligned}

The required common area ,A=2[APOA]

\begin{aligned} &=2 \int_{0}^{2 a} y d x+2 \int_{2 a}^{4 a} y d y \\ &=2 \int_{0}^{2 a} \sqrt{6 a} \sqrt{x} d x+2 \int_{2 a}^{4 a} \sqrt{(4 a)^{2}-x^{2}} d x \\ &=2 \cdot \sqrt{6 a}\left[\frac{2}{3} x 3 / 2\right]_{0}^{2 a}+2\left[\frac{x}{2} \sqrt{(4 a)^{2}-x^{2}}+\frac{1}{2}(4 a)^{2} \sin -1 \frac{x}{4 a}\right]_{2 a}^{4 a} \\ &=2 \cdot \sqrt{6 a} \frac{2}{3}(2 a)^{3 / 2}+2\left[(0-2 a \sqrt{3 a})+8 a^{2}\left(\sin -^{1}-\sin -1 \frac{1}{2}\right)\right] \\ &=2 \cdot 2 \sqrt{3} \cdot \frac{4}{3} a^{2}+2\left[-2 \sqrt{3} a^{2}+8 a^{2}\left(\frac{\pi}{2}-\frac{\pi}{6}\right)\right] \\ &=\frac{16}{3} \sqrt{3} a^{2}-4 \sqrt{3} a^{2}+16 a^{2} \frac{\pi}{3} \\ &=\frac{4 \sqrt{3}}{3} a^{2}+\frac{16 \pi a^{2}}{3} \\ &=\frac{4 a^{2}}{3}(\sqrt{3}+4 \pi) \text { sq.units. } \end{aligned}

Posted by

infoexpert24

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

Board Exam Date Sheet 2025: CBSE, UPMSP, MPBSE, Class 10, 12 board exam dates out; BSEB, CGBSE schedules soon
anam-khan

CBSE Date Sheet 2025 (Out) Live: Class 10, 12 board exam time table at cbse.gov.in; syllabus, sample papers
anam-khan

CBSE Class 12 board exam date sheet 2025 out; exams from February 15 to April 4

Latest Question