If f 0 = 0 , f 3 = 3 and f ′ 3 = 4 , then the value of ∫ 0 1 x f ″ 3 x d x is equal to

Question

If f 0 = 0 , f 3 = 3 and f ′ 3 = 4 , then the value of ∫ 0 1 x f ″ 3 x d x is equal to,

MARKS App · Accepted Answer

Let, Ι = ∫ 0 1 x f ″ 3 x d x Put 3 x = t ⇒ d x = d t 3 Ι = 1 9 ∫ 0 3 t f ″ t d t Ι = 1 9 t f ′ t 0 3 − ∫ 0 3 f ′ t d t = 1 9 3 f ′ 3 − f t 0 3 = 1 9 3 × 4 - 3 = 1

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