The parabola divides the area of the circle in two parts. The area of the smaller part is equal to:...

(c): The points of intersection of and are and . Required area = 2 [ _0^1 2x dx + _1^5 5 - x^2 dx ] = 2 [ | 43 x^3/2 |_0^1 + ( 12 x 5 - x^2 + 52 ^-1 x5 )_1^5 ] = 23 + 5 ^-1 ( 15 ) = 23 +...

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The parabola y^2=4x divides the area of the circle x^2+y^2=5 in two parts. The area of the smaller part is equal to:: Area of Bounded Region (Mathematics) | DivineJEE

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Mathematics
Area of Bounded Region

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Mathematics

The parabola

y^2=4x

divides the area of the circle

x^2+y^2=5

in two parts. The area of the smaller part is equal to:

\frac{1}{3} + 5sin^{-1} (\frac{2}{\sqrt5})

\frac{2}{3} + \sqrt5sin^{-1} (\frac{2}{\sqrt5})

\frac{2}{3} + 5sin^{-1} (\frac{2}{\sqrt5})

\frac{1}{3} + \sqrt5sin^{-1} (\frac{2}{\sqrt5})

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