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JEE Main20208 Jan 2020Evening ShiftMathematicsDefinite IntegrationActual

l i m x → 0 ∫ 0 x t s i n 10 t d t x , is equal to

Options

  1. A0
  2. B1 10
  3. C- 1 5
  4. D- 1 10

Correct answer

A. 0

Step-by-step solution

We have, I = lim x → 0 ∫ 0 x t sin 10 t d t x The given limiting form is the indeterminate form 0 0 . Thus, using Newton-Leibnitz Rule (differentiation under integral sign) and L' Hospital Rule, we get, I = lim x → 0 d d x ∫ 0 x t sin 10 t d t d d x x I = l i m x → 0 x sin 10 x 1 = 0 .

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