Maharashtra State BoardHSC Arts 12th Board Exam
Advertisement Remove all ads

Find the Area of Ellipse `X^2/1 + Y^2/4 = 1` - Mathematics and Statistics

Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads

Find the area of ellipse `x^2/1 + y^2/4 = 1`

 

Advertisement Remove all ads

Solution

Required area = 4 Area (OAPB)

`= int_0^1 ydx`

`:. x^2/1 + y^2/4 = 1`

`:. y =- 2sqrt(1-x^2)`

∴Required area = `4int_0^1 2sqrt(1-x^2)dx`

`= 8[x/2 sqrt(1-x^2) + 1/2 sin^(-1)(x/1)]_0^1`

`= 8[{0+1/2 sin^1 (1)} - 0]`

`= 8 xx 1/2.pi/2 = 2pi
 sq.units"`

Concept: Area of the Region Bounded by a Curve and a Line
  Is there an error in this question or solution?

APPEARS IN

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×