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 16.

Provide solution for RD Sharma Maths Class 12 Chapter 20 Areas of Bounded Region Exercise 20.3 question 16.

Answers (1)

Answer:

\frac{16}{3}\; \text{ab sq. units} .

Hint:

Use basic concepts.

Given:

y^2=4ax and x^2=4by .

Solution: To find area enclosed by

y^2=4ax                ..........(1)

x^2=4by                .........(2)

Equation (1) represents a parabola with vertex (0,0) and axis as x-axis,

Equation (2) represents a parabola with vertex (0,0), and axis as y-axis,

Point of intersection of parabolas are (0, 0) and (4a^{\frac{1}{3}} b^{\frac{2}{3}} , 4a^{\frac{2}{3}}b^{\frac{1}{3}})

 

A rough sketch is given as:

The shaded region is required area  and it is sliced into rectangle of width=\Delta _x  and length(y_2-y_1)

Area of rectangle=(y_1-y_2)\Delta _x

This approximation rectangle slides from x=0 to, x= 4a^{\frac{1}{3}}b^{\frac{2}{3}} , so

Required area = Region OQAPO

\begin{aligned} &=\int_{0}^{4 a^{\frac{1}{4} b^{2}} 3}\left(y_{1}-y_{2}\right) d x \\ &=\int_{0}^{4 a^{\frac{1}{a} b^{2}}}\left(2 \sqrt{a} \cdot \sqrt{x}-\frac{x^{2}}{4 b}\right) d x \\ &=\left[2 \sqrt{a} \cdot \frac{2}{3} x \sqrt{x}-\frac{x^{3}}{12 b}\right]_{0}^{4 a^{\frac{1}{3} b^{2}}} \\ &=\frac{32 \sqrt{a}}{3} \cdot a^{\frac{1}{3}} b^{\frac{2}{3}} a^{\frac{1}{6}} b^{\frac{1}{3}} \\ &=\frac{64 a b^{2}}{12 b} \\ &=\frac{16}{3} a b \text { sq.units } \end{aligned}

Hence the required area is \frac{16}{3}\; \text{ab sq. units} .

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 Time Table 2025 Live: UP Board exams from February 24; CBSE, BSEB date sheet soon
anam-khan

CBSE Date Sheet 2025 Live: Class 10, 12 board exam dates soon; syllabus, sample papers
anam-khan

Extra time in CBSE exams for students with type 1 diabetes: Kerala SHRC seeks report on plea

Latest Question