AP EAMCET201920 Apr 2019Morning ShiftMathematicsArea Under CurvesActual
If the area of the circle (x^2+y^2=2 ) is divided into two parts by the parabola (y=x^2 ), then the area (in sq units) of the larger part is
Options
- A( 3 2 - 1 3 )
- B(6 - 4 3 )
- C( 4 3 - 2 3 )
- D(4 - 1 4 )
Correct answer
A. ( 3 2 - 1 3 )
Step-by-step solution
Given equation of curves (x^2+y^2=2 and y=x^2 ) For point of intersection, on solving the given curves, we get ( aligned & y^2+y-2=0 y^2+2 y-y-2=0 & y(y+2)-1(y+2) =0 & y =1 [ y > 0] aligned ) So, the required area ( aligned & = +2 ₀^1 ( .2-y^2 ) - y ) d y & = +2 [ y 2 2-y^2 + 2 2 ⁻¹ y 2 - 2 3 y^ 3 / 2 ]₀^1 & = +2 [ 1 2 + 4 - 2 3 ]= 3 2 +1- 4 3 aligned ) (= 3 2 - 1 3 sq. units ) Hence, option (1) is correct.