If I = ∫ 0 16 x 1 4 1 + x d x = k + 4 tan − 1 m , then 3 k - m is equal to

Question

If I = ∫ 0 16 x 1 4 1 + x d x = k + 4 tan − 1 m , then 3 k - m is equal to,

MARKS App · Accepted Answer

Let x = t 4 ⇒ d x = 4 t 3 d t ⇒ I = ∫ 0 2 t . 4 t 3 d t 1 + t 2 ⇒ I 4 = ∫ 0 2 t 4 - 1 + 1 1 + t 2 d t ⇒ I 4 = ∫ 0 2 t 2 - 1 t 2 + 1 t 2 + 1 + 1 t 2 + 1 d t = t 3 3 - t + t a n - 1 t 0 2 ⇒ I 4 = 8 3 - 2 + t a n - 1 2 ∴ I = 8 3 + 4 t a n - 1 2 ⇒ k = 8 3 , m = 2 ∴ 3 k - m = 6

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