Question

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

 

Answer 1

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
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