Question

If the line x = α divides the area of region R = {(x,y) ∈ R² : x³ ≤ y ≤ x, 0 ≤ x ≤ 1} into two equal parts, then

(A) 0 < α ≤ 1/2

(B) 1/2 < α < 1

(C) 2α⁴ - 4α² + 1 = 0

(D) α⁴ + 4α² - 1 = 0

Answer 1

(B) 1/2 < α < 1

(C) 2α4 - 4α2 + 1 = 0