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NTA Abhyas JEE Main2020MathematicsDefinite IntegrationPractice

Consider I = ∫ 0 1 d x 1 + x 5 . Then, I satisfies

Options

  1. AI > 1
  2. BI = 1
  3. CI < 1
  4. DI + 1 < 0

Correct answer

C. I < 1

Step-by-step solution

As, x ∈ 0 , 1 x 5 ∈ 0 , 1 ∴ 1 + x 5 ∈ 1 , 2 ⇒ 1 + x 5 > 1 ∴ ∫ 0 1 d x 1 + x 5 < ∫ 0 1 1 d x ⇒ I < 1

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