# The area enclosed by the curve y2 + x4 = x2 is-(a)2/3(b)4/3(c)8/3(d)10/3

Arun
25757 Points
4 years ago
Dear student

This curve is symmetrical along the x and y axis, so we can integrate the area in the first quadrant and multiply it by 4.

y = x(√(1-x^2))

A = ∫ 0->1 x(√(1-x^2)) dx

A = -1/3 (1-x^2)^(3/2) | 0->1

A = 1/3

Total Area is 1/3 x 4 = 4/3