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in Integrals calculus by (54.8k points)

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 included between the line y = x - 1 and the curve y = f(x) is 

(A) 2/5 sq. units 

(B) 3/10 sq. units 

(C) 7/10 sq. units 

(D) 7/5 sq. units

1 Answer

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Best answer

Answer is (B) 3/10 sq. units

x = 1 is a root of f(x) and also a root of 1st, 2nd and 3rd derivatives of f(x). Hence, f(x) has x = 1 repeated root 4 times so f(x) = (x - 1)4. Therefore,

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