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If Ι 1 = ∫ - 1 2 x s i n x 1 - x d x and Ι 2 = ∫ - 1 2 s i n x 1 - x d x , then Ι 1 Ι 2 is equal to

Options

  1. A2
  2. B1 2
  3. C1
  4. D1 3

Correct answer

B. 1 2

Step-by-step solution

Ι 1 = ∫ - 1 2 x s i n x ( 1 - x ) d x Ι 1 = ∫ - 1 2 1 - x s i n 1 - x x d x Ι 1 = ∫ - 1 2 s i n x 1 - x d x - ∫ - 1 2 x s i n 1 - x x d x Ι 1 = Ι 2 - Ι 1 2 Ι 1 = Ι 2 Ι 1 Ι 2 = 1 2

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