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JEE Main202125 Feb 2021Morning ShiftMathematicsDefinite IntegrationActual

The value of ∫ - 1 1 x 2 e x 3 d x , where t denotes the greatest integer ≤ t , is :

Options

  1. Ae + 1 3
  2. Be - 1 3 e
  3. C1 3 e
  4. De + 1 3 e

Correct answer

D. e + 1 3 e

Step-by-step solution

I = ∫ - 1 1 x 2 e x 3 d x = ∫ - 1 0 x 2 e x 3 d x + ∫ 0 1 x 2 e x 3 d x = ∫ - 1 0 x 2 e - 1 d x + ∫ 0 1 x 2 e 0 d x = 1 e × x 3 3 0 - 1 + x 3 3 0 1 = 1 e × 0 - - 1 3 + 1 3 = 1 3 e + 1 3 = 1 + e 3 e

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