Home
Class 12
MATHS
Area lying in the first quadrant and bou...

Area lying in the first quadrant and bounded by the circle `x^2+y^2=4`and the lines `x= 0 a n dx= 2`is(A) `pi` (B) `pi/2` (C) `pi/3` (D) `pi/4`

A

`pi`

B

`(pi)/(2)`

C

`(pi)/(3)`

D

`(pi)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
A
The region bounded by the circle and lines `x=0` and `x=2` in first quadrant is shown by shaded region in the figure.

` :. "Required area" =int_(0)^(2)ydx=int_(0)^(2)sqrt(4-x^(2))dx`
` [(x)/(2)sqrt(4-x^(2))+(4)/(2)"sin"^(-1)((x)/(2))]_(0)^(2)`
`=0+2sin^(-1)(1)-0`
`=2xx(pi)/(2)=pi` sq. units.
Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF INTEGRALS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 8.2|7 Videos

  • APPLICATIONS OF INTEGRALS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos

  • APPLICATIONS OF INTEGRALS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 8 C Questions For Competitive Examinations|10 Videos

  • APPLICATIONS OF DERIVATIVES

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|24 Videos

  • Continuity and Differentiability

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|23 Videos

Similar Questions

Explore conceptually related problems

Area lying in the first quadrant and bounded by the circle x^2+y^2=4 and the lines x= 0 and x= 2 is:

Area lying in the first quadrant and bounded by the circle x^(2)+y^(2)=4 the line x=sqrt(3)y and x-axis , is

Find the area of the figure lying in the first quadrant and bounded by the curves y^2=4x, x^2=4y .

Find the area of the region lying in the first quadrant and bounded by y=4x^2 , x = 0, y = 1 a n d y = 4 .

If A_n be the area bounded by the curve y=(tanx)^n and the lines x=0,\ y=0,\ x=pi//4 , then for n > 2.

The area bounded by the curves x^2+y^2=1,x^2+y^2=4 and the pair of lines sqrt3 x^2+sqrt3 y^2=4xy , in the first quadrant is (1) pi/2 (2) pi/6 (3) pi/4 (4) pi/3

The angles at which the circles (x-1)^2+y^2=10a n dx^2+(y-2)^2=5 intersect is pi/6 (b) pi/4 (c) pi/3 (d) pi/2

The angle of intersection of the curves y=2\ sin^2x and y=cos2\ x at x=pi/6 is (a) pi//4 (b) pi//2 (c) pi//3 (d) pi//6

The angle between the tangents to the curve y=x^2-5x+6 at the point (2, 0) and (3, 0) is (a) pi/2 (b) pi/3 (c) pi (d) pi/4

The angle between the tangents to the curve y=x^2-5x+6 at the point (2, 0) and (3, 0) is pi/2 (b) pi/3 (c) pi (d) pi/4