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Let Ι 1 = ∫ 0 1 e x 2 d x and Ι 2 = ∫ 0 1 2 x 2 e x 2 d x , then the value of Ι 1 + Ι 2 is equal to

Options

  1. A1
  2. B2
  3. Ce
  4. De 2

Correct answer

C. e

Step-by-step solution

Ι 2 = ∫ 0 1 2 x 2 e x 2 d x = ∫ 0 1 2 x e x 2 x d x Using integration by parts, Ι 2 = x e x 2 0 1 - ∫ 0 1 e x 2 d x Ι 2 + Ι 1 = e

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