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If I = ∫ d x x 5 2 1 + x 7 2 3 = k f x + c , where c is the integration constant and f 1 = 1 2 1 6 , then the value of f 2 is equal to

Options

  1. A6 2 3 1 6
  2. B6 3 2 1 6
  3. C2 3 1 6
  4. D2 3 6

Correct answer

C. 2 3 1 6

Step-by-step solution

The given integral is I = ∫ d x x 6 1 + x x 7 2 1 3 ⇒ I = ∫ d x x 2 1 + 1 x 7 6 Let, 1 + 1 x = t ⇒ - d x x 2 = d t ⇒ I = ∫ - d t t 7 6 = 6 t - 1 6 + c = 6 x x + 1 1 6 + c ∴ f x = x x + 1 1 6 ⇒ f 2 = 2 3 1 6

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