Let P_ 1 : y=4 x^ 2 and P_ 2 : y=x^ 2 +27 be two parabolas. If the area of the bounded region enclosed between P_ 1 and P_ 2 is six times the area of the bounded region enclosed between the line y= x, 0 and P_ 1 , then is equal to :

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Let P_ 1 : y=4 x^ 2 and P_ 2 : y=x^ 2 +27 be two parabolas. If the area of the bounded region enclosed between P_ 1 and P_ 2 is six times the area of the bounded region enclosed between the line y= x, >0 and P_ 1 , then is equal to :

Quantrex Academy · Accepted Answer

Correct answer: A. 12

Area bounded between P_1 & P_2 is _ -3 ^ 3 ((x^2 + 27) - (4x^2)) \, dx (P.O.I. of P_1 & P_2 is x = 3) = 2 _ 0 ^ 3 (27 - 3x^2) \, dx = 2[27x - x^3]_ 0 ^ 3 = 2[81 - 27] = 108 Area bounded between P_1 & 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

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