Home
Class 12
MATHS
Find the area enclosed by the circle x^...

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

Text Solution

Verified by Experts

Given equation of circle is:
`x^2+y^2=a^2`
`y^2 = a^2-x^2`
=> `y = sqrt(a^2-x^2)`
Area of circle = `4 xx` area of first quadrant
= `4int _0^a ydx`
= `4int _0^a sqrt(a^2-x^2)dx`
= `4[ x/(2) sqrt(a^2-x^2) + a^2/(2) sin^-1(x/a)]_0^a`
= `4[ a^2/(2) sin^-1 -0]` = `2a^2 . pi/2 = pia^2` square unit
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF INTEGRALS

    NCERT ENGLISH|Exercise Exercise 8.1|13 Videos

  • APPLICATION OF INTEGRALS

    NCERT ENGLISH|Exercise EXERCISE 8.2|7 Videos

  • APPLICATION OF INTEGRALS

    NCERT ENGLISH|Exercise EXERCISE 8.2|7 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

Find the area enclosed between the circle x^2+y^2=25 and the straight line x+y=5 .

Find the area enclosed by the curves y=4x^2 and y^2=2x .

Find the area enclosed by the curves x^2=y , y=x+2,

Find the area enclosed by the circle of radius a.

Find the area enclosed by circle x^(2)+y^(2)=4 , parabola y=x^(2)+x+1 , the curve y=[sin^(2)x/4+cos x/4] and X-axis (where,[.] is the greatest integer function.

Find the area enclosed by the curves x^2=y , y=x+2 and x-axis

Find the area enclosed by the graph of x^2y^2-9x^2-25 y^2+225=0

Find the area enclosed by the graph of x^2y^2-9x^2-25 y^2+225=0 .

The area enclosed by the curve y^2 +x^4=x^2 is

Find the area enclosed by the curves 3x^2+5y=32a n dy=|x-2|dot