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MHT CET2019Evening ShiftMathematicsDefinite IntegrationActual

∫ 0 1 x 1 - x 5 d x = … … .

Options

  1. A1 5
  2. B1 42
  3. C1 13
  4. D13 42

Correct answer

B. 1 42

Step-by-step solution

Let = l = ∫ 0 1 x 1 - x 5 d x Put 1 - x = t ⇒ x = 1 - t ⇒ - d x = d t ⇒ d x = - d t When x = 0 ' , then t = 1 and When x = 1 , t h e n t = 0 ∴ l ∫ 1 0 1 - t t 5 - d t = ∫ 0 1 t 5 - t 6 d t = t 6 6 - t 7 7 = 1 6 1 6 - 1 7 1 7 = 7 - 6 42 = 1 42

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