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JEE Main20199 Apr 2019Evening ShiftMathematicsDefinite IntegrationActual

If f : R → R is a differentiable function and f 2 = 6 , then l i m x → 2 ∫ 6 f x 2 t d t x - 2 is:

Options

  1. A0
  2. B2 f ' 2
  3. C24 f ' 2
  4. D12 f ' 2

Correct answer

D. 12 f ' 2

Step-by-step solution

The given limit can be written as l = lim x → 2 ∫ 6 f x 2 t d t x - 2     Applying L' Hospital’s rule i.e. if l = lim x → a g x h x and lim x → a g x → 0   &   lim x → a h x → 0 , then l = lim x → a g ' x h ' x l = l i m x → 2 d d x ∫ 6 f x 2 t d t 1 Now, applying Newton's Leibnitz rule i.e. d d x ∫ a b g x d x = g b · b ' - g a · a ' , we get ⇒ l = lim x → 2 2 f x · f ' x - 0 &

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