Question

Consider a region R = {(x,y)∈R² : x² ≤ y ≤ 2x}. If a line y = α divides the area of region R into two equal parts, then which of the following is true ?

(1) α³ - 6α² + 16 = 0

(2) 3α² – 8α^3/2 + 8 = 0

(3) α³ –  6α^3/2 - 16 = 0

(4) 3α² – 8α^3/2 + 8 = 0

Answer 1

Answer is (4) 3α² – 8α^3/2 + 8 = 0

* y ≥ x² ⇒ upper region of y = x² 

y ≤ 2x ⇒ lower region of y = 2x

According to ques, area of OABC = 2 area of OAC