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JEE Main2003MathematicsDefinite IntegrationActual

The value of _ x 0 ₀^ x^2 ^2 t d t x x is

Options

  1. A0
  2. B3
  3. C2
  4. D1

Correct answer

D. 1

Step-by-step solution

Lim _ x 0 d d x ₀^ x^2 ^2 t d t d d x (x x) = Lim _ x 0 ^2 x^2 2 x x+x x (by L'Hospital rule) Lim _ x 0 2 ^2 x^2 ( x x + x ) = 2 1 1+1 =1

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