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JEE Main202124 Feb 2021Morning ShiftMathematicsDefinite IntegrationActual

lim x → 0 ∫ 0 x 2 sin t d t x 3 is equal to:

Options

  1. A0
  2. B2 3
  3. C3 2
  4. D1 15

Correct answer

B. 2 3

Step-by-step solution

lim x → 0 + ∫ 0 x 2 sin t d t x 3 = lim x → 0 + sin x 2 x 3 x 2 = lim x → 0 + sin x x × 2 3 = 2 3

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