Home
Class 12
MATHS
Find the area of the smaller part of ...

Find the area of the smaller part of the circle `x^2+y^2=a^2` cut off by the line `x=a/(sqrt(2))`

A

`a^4[pi/5 - 1/3]`

B

`a^2[pi/4 - 1/2]`

C

`a^2[pi/3 - 1/4]`

D

`a^3[pi/3 - 1/2]`

Text Solution

Verified by Experts

The correct Answer is:
B
require Area= `int ydx`
`= int_(a/sqrt2)^a 2 sqrt(a^2 - x^2) dx`
`=> x = aSin theta`
`dx= a cos theta d theta`
when `x=a/sqrt2, sin theta= 1/sqrt2`
`theta= pi/4`
when `x=a, sin theta = 1`
`theta= pi/2`
...
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF INTEGRALS

    NCERT ENGLISH|Exercise EXERCISE 8.2|7 Videos

  • APPLICATION OF INTEGRALS

    NCERT ENGLISH|Exercise SOLVED EXAMPLES|15 Videos

  • APPLICATION OF DERIVATIVES

    NCERT ENGLISH|Exercise SOLVED EXAMPLES|51 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    NCERT ENGLISH|Exercise EXERCISE 5.7|17 Videos

Similar Questions

Explore conceptually related problems

The area of the smaller part of the circle x^(2)+y^(2)=2 cut off by the line x=1 is

Find the area of the smaller portion of the circle x^2+y^2=4 cut off by the line x^2=1

The area of the smaller portion of the circle x^2+y^2=4 cut off the line x+y=2 is

Find the area of the portion of the parabola y^2=4x cut off by the line y=x .

The range of values of r for which the point (-5+r/sqrt(2),-3+r/sqrt(2)) is an interior point of the major segment of the circle x^2+y^2=16 , cut-off by the line x+y=2 , is:

Find the area of the circle x^2+y^2=a^2 with radius a

Find the area enclosed by the circle x^2+y^2=a^2 .

Find the middle point of the chord of the circle x^2+y^2=25 intercepted on the line x-2y=2

Find the ratio of the areas of the portion between the circle x^2 + y^2 = a^2 and straight line x = a /2

Find the equation of image circle of the circle x^(2)+y^(2)-2x=0 in the line x+y-2=0