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 RD Sharma Maths Class 12 Chapter 20 Areas of Bounded Regions exercise 20.3 question 27.

Need solution for RD Sharma Maths Class 12 Chapter 20 Areas of Bounded Regions exercise 20.3 question 27.

Answers (1)

Answer:

\frac{64}{3}\; \text{sq. units}

Hint:

use concept.

Given:

The given equations are y=x-1 and (y-1)^2=4(x+1)

Solution:

We have.y=x-1 and (y-1)^2=4(x+1)

\therefore (x-1-1)^2=4(x+1)

\begin{aligned} &(x-2)^{2}=4(x+1) \\ &x^{2}+4-4 x=4 x+4 \\ &x^{2}+4-4 x-4 x-4=0 \\ &x^{2}-8 x=0 \\ &x=0 \text { or } x=8 \\ &\therefore y=-1 \text { or } 7 \end{aligned}

Consider a horizontal strip of length \left |x_2-x_1 \right |  and width dy where P(x_2,y)  lies on straightline and Q(x_1,y) lies on the parabola.

Area of approximating rectangle=\left |x_2-x_1 \right |  and it moves from y =1 to y =- 7

\text { Required area }=\operatorname{area}(O A D O)=\int_{1}^{7}\left|x_{2}-x_{1}\right| d y

\begin{aligned} &=\int_{-1}^{7}\left|x_{2}-x_{1}\right| d y \ldots \ldots \ldots\left\{\therefore\left|x_{2}-x_{1}\right|=x_{2}-x_{1} \text { as } x_{2}>x_{1}\right\} \\ &=\int_{-1}^{7}\left[(1+y)-\frac{1}{4}\left\{(y-1)^{2}-4\right\}\right] d y \\ &=\int_{-1}^{7}\left\{1+y-\frac{1}{4}(y-1)^{2}+1\right\} d y \\ &=\int_{-1}^{7}\left\{2+y-\frac{1}{4}(y-1)^{2}\right\} d y \end{aligned}

\begin{aligned} &=\left[2 y+\frac{y^{2}}{2}-\frac{1}{12}(y-1)^{3}\right]_{-1}^{7} \\ &=\left[14+\frac{49}{2}-\frac{1}{2} \times 6 \times 6 \times 6\right]-\left[-2+\frac{1}{2}+\frac{1}{12} \times 2 \times 2 \times 2\right] \\ &=\left[14+\frac{49}{2}-18\right]-\left[-2+\frac{1}{2}+\frac{2}{3}\right] \\ &=\left[\frac{41}{2}+\frac{5}{6}\right] \\ &=\frac{64}{3} \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

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
anam-khan

When will CBSE Board exam 2025 date sheet be released for Class 10, 12?

Latest Question