The area of the smaller region bounded by the ellipse x^2 + 4y^2 = 5 and the parabola y = x^2 is equal to:

Step-by-step solution

Given equations of the curves are: x^2 + 4y^2 = 5 (Ellipse) y = x^2 (Parabola) To find the points of intersection, substitute x^2 = y into the equation of the ellipse: y + 4y^2 = 5 4y^2 + y - 5 = 0 (4y + 5)(y - 1) = 0 Since y = x^2 0 , we have y = 1 . For y = 1 , x^2 = 1 x = 1 . The points of intersection are (1, 1) and (-1, 1) . The smaller region bounded by these curves lies in the upper half-plane, bounded above by the ellipse and below by the parabola. Due to symmetry about the y-axis, the required area A is tw