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JEE Main201912 Apr 2019Morning ShiftMathematicsDefinite IntegrationActual

Let f : R → R be a continuous and differentiable function such that f 2 = 6 and f ' 2 = 1 48 . If ∫ 6 f ( x ) 4 t 3 d t = x - 2 g x , then l i m x → 2 g x is equal to

Options

  1. A24
  2. B18
  3. C12
  4. D36

Correct answer

B. 18

Step-by-step solution

l i m x → 2 g x = l i m x → 2 ∫ 6 f x 4 t 3 d t x - 2             0 0   form . By using L'Hospital rule = l i m x → 2 4 . f 3 ( x ) ⋅ f ' x 1 = 4 f 3 2 f ' 2 = 4 × 6 × 6 × 6 × 1 48 = 18 .

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