KCET2019MathematicsArea Under Curves
The area of the region above ( X )-axis included between the parabola ( y²=x ) and the circle ( x²+y²=2 x ) in square units is
Options
- A( 3 2 - 4 )
- B( I 4 - 2 3 )
- C( I 4 - 3 2 )
- D( 2 3 - 4 )
Correct answer
B. ( I 4 - 2 3 )
Step-by-step solution
(B) [ array l y²=x (1) x²+y²=2 x (2) array ] Equation (2) is a circle with centre ( (1,0) ) and radius ( 1 ). Solving (1) and (2), we get the points of intersection ( (0,0) ) and ( (1,1) ) ( (x-1)²+y²=1 ) ( y²=x ) ( (x-1)²+x=1 ) ( x²-x=0 ) ( x(x-1)=0 ) ( x=0, x=1 ) area ( = ₀¹ 1-(x-1)² - x d x ) ( =- [ x^ 3 2 3 2 ]₀¹+ ) ( [ x-1 2 1-(x-1)² + 1 2 ⁻¹(x-1) ]¹ )