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in Integrals calculus by (36.9k points)

Let f: (0,∞) → R and F(x) = ∫f(t) dt for t ∈ [0,x] and F(x2) = x2 (x + 1), then f(4) equals 

(a) 5/40 

(b) 7 

(c) 4 

(d) 2

1 Answer

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by (38.6k points)
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Best answer

Answer (c) 4

Given 

F'(x) = f(x) 

Also, F(x2) = x2(x + 1) = x3 + x

F'(x2).2x = 3x2 + 2x 

F'(x2) = (3x2/2x) + 1 = (3/2x) + 1 

f(x2) = (3/2x) + 1

Putting x = 2, we get 

f(4) = (3/2).2 + 1 

= 4 

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