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JEE Main2005MathematicsDefinite IntegrationActual

Let f: R R be a differentiable function having f(2)=6, f^ (2)= ( 1 48 ) . Then _ x 2 ₆^ f(x) 4 t^3 x-2 d t equals

Options

  1. A24
  2. B36
  3. C12
  4. D18

Correct answer

D. 18

Step-by-step solution

_ x 2 ₀^ f(x) 4 t^3 x-2 d t Applying L Hospital rule aligned & _ x 2 [4 f(x)^2 f^ (x) ]=4 f(2)^3 f^ (2) & =4 6^3 1 48 =18 . aligned

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