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JEE Main20206 Sep 2020Morning ShiftMathematicsIndefinite IntegrationActual

If I 1 = ∫ 0 1 1 - x 50 100 d x and I 2 = ∫ 0 1 1 - x 50 101 d x such that I 2 = α I 1 then α equals to :

Options

  1. A5049 5050
  2. B5050 5049
  3. C5050 5051
  4. D5051 5050

Correct answer

C. 5050 5051

Step-by-step solution

Given α = I 2 I 1 = ∫ 0 1 1 - x 50 101 d x ∫ 0 1 1 - x 50 100 d x Now, I 2 = ∫ 0 1 1 - x 50 1 - x 50 100 d x I 2 = I 1 - ∫ 0 1 x . x 49 1 - x 50 100 d x I 2 = I 1 - - x 1 - x 50 101 5050 0 1 - ∫ 0 1 1 - x 50 101 5050 d x I 2 = I 1 - I 2 5050 ⇒ α = I 2 I 1 = 5050 5051

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