The area of the region in the first quadrant inside the circle x^2+y^2=8 and outside the parabola y^2=2 x is equal to :

Step-by-step solution

Required area = Ar ( circle from 0 to 2 )- ar ( para from 0 to 2 ) aligned & = ₀^2 8-x^2 d x- ₀^2 2 x d x & = [ x 2 8-x^2 + 8 2 ⁻¹ x 2 2 ]₀^2- 2 [ x x 3 / 2 ]₀^2 & = 2 2 8-4 + 8 2 ⁻¹ 2 2 2 - 2 2 3 (2 2 -0) & 2+4 4 - 8 3 = - 2 3 aligned