Definite IntegrationHard

Question

The area of the region bounded by the curve a4y2 = (2a - x) x5 is to that of the circle whose radius is a, is given by the ratio

Options

A.4 : 5
B.5 : 4
C.2 : 3
D.3 : 2

Solution

       
a4y2 = (2a - x) x5 = 2ax5 - x6             
here (2a - x) . x5 ≥ 0
⇒   x ∈ [0, 2a]
A = 2 dx
. x2 dx
put x - a = a cos θ
then   A = a sin . θ a2(1 + cos θ)2. (-a sin θ)dθ = 2a2dθ
= 2a2
A = 2a2 π22
∴  = 5 : 4

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