If I = ∫ 1 + x 4 1 - x 4 3 2 d x = 1 f x + C (where, C is the constant of integration) and f 2 = - 15 4 , then the value of 2 f 1 2 is

Question

If I = ∫ 1 + x 4 1 - x 4 3 2 d x = 1 f x + C (where, C is the constant of integration) and f 2 = - 15 4 , then the value of 2 f 1 2 is,

MARKS App · Accepted Answer

Given integral is I = ∫ 1 x 3 + x 1 x 2 - x 2 3 2 d x Let 1 x 2 - x 2 = t ⇒ - 2 x 3 - 2 x d x = d t ∴ I = - 1 2 ∫ d t t 3 2 = t - 1 2 + C = 1 1 x 2 - x 2 + C ∴ f x = 1 x 2 - x 2 ⇒ f 1 2 = 2 - 1 2 = 3 2 ⇒ 2 f 1 2 = 3

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