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NTA Abhyas JEE Main2020MathematicsDefinite IntegrationPractice

The integral I = ∫ e e + 1 1 + x 2 1 + x 3 d x satisfies

Options

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

Correct answer

D. I < 1

Step-by-step solution

x ∈ e , e + 1 ⇒ x 2 < x 3 ⇒ 1 + x 2 1 + x 3 < 1 ⇒ ∫ e e + 1 1 + x 2 1 + x 3 d x < ∫ e e + 1 1 d x ⇒ I < x e e + 1 ⇒ I < 1

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