If the area of the region x , y : x 2 3 + y 2 3 ≤ 1 , x + y ≥ 0 , y ≥ 0 is A , then 256 A π is

Step-by-step solution

Plotting the diagram of given data we have, Now finding limit by diagram, we get x 2 3 + x 2 3 = 1 ⇒ x = ± 1 2 2 So total area will be given by, A = ∫ - 1 2 2 0 1 - x 2 3 3 2 d x - 1 2 × 1 2 2 × 1 2 2   + ∫ 0 1 1 - x 2 3 3 2 d x Now for solving ∫ 1 - x 2 3 3 2 d x Let x = sin 3 θ = ∫ 1 - sin 2 θ 3 2 · 3 sin 2 θ cos θ d θ = ∫ 3 sin 2 θ cos 4 θ d θ = 3 ∫ sin 2 θ cos 4 θ d θ Now putting the limit a