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JEE Advanced2014MathematicsDefinite IntegrationActual

Paragraph: Given that for each a (0,1) , _ h 0⁺ _ h ^ 1-h t^ -a (1-t)^ a-1 d t exists. Let this limit be g(a) . In addition, it is given that the function g(a) is differentiable on (0,1) . Question: The value of g^ ( 1 2 ) is

Options

  1. Aπ 2
  2. Bπ
  3. C- π 2
  4. D0

Correct answer

D. 0

Step-by-step solution

We have g a = g 1 - a and g is differentiable. ∴ g ' a = - g ' 1 - a Hence g ′ 1 2 = 0 .

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