If f x is a continuous function and ∫ x 2 x 4 t 3 f t d t = s i n 2 π x , then f 1 is equal to

Question

If f x is a continuous function and ∫ x 2 x 4 t 3 f t d t = s i n 2 π x , then f 1 is equal to, 1, – 1, π, - π

MARKS App · Accepted Answer

Differentiating using Leibnitz rule, we get, x 12 f x 4 4 x 3 - x 6 f ( x 2 ) 2 x = 2 π c o s π x Putting x = 1 ⇒ 4 f 1 - 2 f 1 = 2 π ⇒ 2 f 1 = 2 π ⇒ f 1 = π

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