The parabolas y 2 = 4 x and x 2 = 4 y divide the square region bounded by the lines x = 4 , y = 4 and the coordinate axes. If S 1 , S 2 , S 3 are respectively the areas of these parts numbered from top to bottom of the square region, then S 1 : S 2 : S 3 is

Step-by-step solution

y 2 = 4 x and x 2 = 4 y are symmetric about line y = x ⇒ Area bounded between y 2 = 4 x and y = x is ∫ 0 4 2 x - x d x = 8 3 ⇒ A S 2 = 16 3 and A S 1 = A S 3 = 16 3 Area of rectangle − S 2 2 ⇒ A S 1 : A S 2 : A S 2 : : 1   : 1   : 1 .