Let f(x) be a polynomial of degree 4 satisfying (∫A(t)B(t)dt for t∈[1, x])(∫C(t)D(t)dt for t∈[1, x]) - (∫A(t)C(t)dt for t∈[1, x])(∫B(t)D(t)dt for t∈[1, x]) = f(x) ∀ x ∈ R
where A(x), B(x), C(x) and D(x) are non-constant continuous and differentiable functions. It is given that the leading coefficient (coefficient of x4) of f(x) is 1.
The area of the smaller region intercepted between the curve y = f(x) and x2 + y2 = 1 is
(A) π/4 - 1/5 sq. units
(B) π/4 sq. units
(C) π/4 + 1/5 sq. units
(D) π/2 + 1/5 sq. units
