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Let f x = 2 x + 1 and g x = ∫ f x x 2 x + 1 2 d x . If 6 g 2 + 1 = 0 , then g - 1 2 is equal to

Options

  1. A4
  2. B- 4
  3. C3
  4. D2

Correct answer

A. 4

Step-by-step solution

g x = ∫ x + 1 2 - x 2 x 2 x + 1 2 d x = ∫ 1 x 2 - 1 x + 1 2 d x = - 1 x + 1 x + 1 + c = - 1 x x + 1 + c g 2 = - 1 6 + c = - 1 6 ⇒ c = 0 Hence, g - 1 2 = 4

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