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JEE Main2012MathematicsDefinite IntegrationActual

If _e^x t f(t) d t= x-x x- x^2 2 , for all x R- 0 , then the value of f ( 6 ) is

Options

  1. A1/2
  2. B1
  3. C0
  4. D-1 / 2

Correct answer

D. -1 / 2

Step-by-step solution

Let _e^x t f(t) d t= x-x x- x^2 2 By using Leibnitz rule, we get aligned & d d x [ _e^x t f(t) d t ]= d d x [ x-x x- x^2 2 ] & x f(x)-e f(e) 0=x x-x aligned Now, put x= 6 , we get aligned & 6 f ( 6 )= 6 6 - 6 & f ( 6 )= 6 -1= 1 2 -1=- 1 2 aligned

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