JEE Advanced2017MathematicsArea Under CurvesActual
If the line x = α divides the area of the region R = x , y ∈ R 2 : x 3 ≤ y ≤ x , 0 ≤ x ≤ 1 into two equal parts, then
Options
- A1 2 < α < 1
- Bα 4 + 4 α 2 - 1 = 0
- C0 < α ≤ 1 2
- D2 α 4 - 4 α 2 + 1 = 0
Correct answer
A. 1 2 < α < 1
Step-by-step solution
A = ∫ 0 1 x - x 3 d x = 1 4 Area of curvilinear triangle O P Q = A 2 = 1 8 ⇒ ∫ 0 1 x - x 3 d x = 1 8 ⇒ 2 α 4 - 4 α 2 + 1 = 0 ⇒ α 2 - 1 2 = 1 2 ⇒ α 2 = 2 - 1 2 so α lies between 0.5 and 1