Definite IntegrationHard

Question

Area of the curve y2 = (7 - x) (5 + x) above x-axis and between the ordinates x = - 5 and x = 1 is

Options

A.9π
B.18π
C.15π
D.none

Solution

    
y2 = (7 - x) (5 + x)  at y = 0,   x = 7, - 5
(x - 1)2 + y2 = (6)2  centre (1,0)
From the figure it is clear that area is
=
=
= [(0 + 0) - (0 + 18sin-1(-1))] = 9π

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