Let P₁: y=4 x² and P₂: y=x²+27 be two parabolas. If the area of the bounded region enclosed between P₁ and P₂ is six times the area of the bounded region enclosed between the line y= x, >0 and P₁ , then is equal to :

Step-by-step solution

Area bounded between P₁ & P₂ is _ -3 ³ ((x^2 + 27) - (4x^2)) , dx (P.O.I. of P₁ & P₂ is x = 3 ) = 2 ₀³ (27 - 3x^2) , dx = 2[27x - x^3]₀³ = 2[81 - 27] = 108 Area bounded between P₁ & L is 18 sq. units (Area between x^2 = 4ay & line x = my ) is 8a^2 3m^3 Area between x^2 = y 4 & x = y is 8 ( 1 16 )^2 3 ( 1 )^3 = 18 8 16 16 3 ^3 = 18 ^3 = 2^6 3^3 = 12