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If Ι = ∫ d x x 3 x 8 + 1 3 / 4 = λ 1 + x 8 1 4 x 2 + c (where c is the constant of integration), then the value of λ is equal to

Options

  1. A2
  2. B1 2
  3. C- 2
  4. D- 1 2

Correct answer

D. - 1 2

Step-by-step solution

Ι = ∫ x - 9 1 + x - 8 3 4 d x Let, 1 + x - 8 = t - 8 x - 9 d x = d t Ι = ∫ - d t 8 t 3 / 4 = - 1 8 ∫ t - 3 / 4 d t = - 1 8 t 1 / 4 1 4 + c = - 1 + x - 8 1 / 4 2 + c = - 1 + x 8 1 / 4 2 x 2 + c ⇒ λ = - 1 2

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