If ∫ f x d x = 3 f x 2 + c (where c is the constant of integration) and f 1 = 1 6 , then f 6 π is equal to

Question

If ∫ f x d x = 3 f x 2 + c (where c is the constant of integration) and f 1 = 1 6 , then f 6 π is equal to, π 2, π, π 3, π 6

MARKS App · Accepted Answer

Differentiating the given integral with respect to ‘ x ’ , we get, f x = 6 f x ⋅ f ′ x or 1 6 = f ′ x On integrating, we get, ∫ 1 6 d x = ∫ f ′ x d x ⇒ x 6 = f x + c As f 1 = 1 6 ⇒ c = 0 ⇒ f x = x 6 ⇒ f 6 π = π

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