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:

Question

Accepted Answer

Correct answer: C. (c) y^2=4xx^2+y^2=5 ∴ Area of shaded region as shown in the figure will be A_1= _0^1 0.05em 4x dx+ _1^ 5 0.05em 5-x^2 dx = 43 (x^ 32 )_0^1+( x2 5-x^2+ 52 sin^-1 ⁡ x 5)_1^ 5 = 13+ 5 4- 52 sin^-1 ⁡ ( 1 5 ) ∴ Required Area=2 A_1 = 23+ 5 2-5 sin^-1 ⁡ ( 1 5 ) = 23+5( 2- sin^-1 ⁡ 1 5) = 23+5 cos^-1 ⁡ 1 5 = 23+5 sin^-1 ⁡ ( 2 5 )

$The parabola y^{2} = 4 x divides the area of the circle x^{2} + y^{2} = 5 in two parts. The area of the smaller part is equal to:$

Solution

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