Home
Class 12
MATHS
The area of the region described by A = ...

The area of the region described by `A = {(x,y) : x^2 + y^2 lt= 1and y^2 lt= 1- x}` is

A

`(pi)/(2)+(4)/(3)`

B

`(pi)/(2)-(4)/(3)`

C

`(pi)/(2)-(2)/(3)`

D

`(pi)/(2)+(2)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
D
`x^(2)+y^(2)le1" represents the rgeion inside the circle "x^(2)+y^(2)=1.`

`y^(2)le1-x`, represents the region inside parabola `y^(2)=1-x` towards focus.
The common region is as shown in the figure.
The area of shaded region
= Area of semicircle ADOBA+ Area of region ODCBO
`=(pi)/(2)+2overset(1)underset(0)int(1-y^(2))dy`
`=(pi)/(2)+2[y-(y^(3))/(3)]_(0)^(1)`
`=(pi)/(2)+2[1-(1)/(3)]`
`=(pi)/(2)+(2)/(3)`
Promotional Banner

Topper's Solved these Questions

  • AREA

    CENGAGE PUBLICATION|Exercise Single Correct Answer Type|30 Videos

  • AREA

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer Type|3 Videos

  • AREA

    CENGAGE PUBLICATION|Exercise Numerical Value Type|18 Videos

  • APPLICATIONS OF DERIVATIVES

    CENGAGE PUBLICATION|Exercise Subjective Type|2 Videos

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise Comprehension|11 Videos

Similar Questions

Explore conceptually related problems

The area of the region described by A={(x,y):x^(2)+y^(2)le1" and "y^(2)le1-x} is-

The area (in sq. units) of the region described by {(x,y):y^(2)le2x" and "yge4x-1} is-

The area (in sq. units) of the region described by {x,y):y^(2)le2x and yge4x-1} is

The area of the region bounded by y=|x| and y=-|x|+2 is-

The area of the region R={(x,y):|x| le|y| and x^2+y^2le1} is

Find the area of the region { (x,y): x^(2)lt y lt |x| }

Find the area of the region {(x , y): y^2lt=4x ,4x^2+4y^2lt=9}

Find the area of the region {( x,y): x^(2)lt ylt x}

The area (in sq units) of the region {(x, y) : y^2 gt= 2x and x^2 + y^2 lt= 4x, x gt= 0, y gt= 0} is