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NTA Abhyas JEE Main2020MathematicsDefinite IntegrationPractice

The value of I = ∫ - 1 1 x sin ⁡ ( π x ) d x is (where [·] denotes the greatest integer function)

Options

  1. Aπ
  2. B2 π
  3. C0
  4. D- π

Correct answer

C. 0

Step-by-step solution

I = 2 ∫ 0 1 x sin ( π x ) d x Now, x sin ( π x ) ∈ 0 , 1 as x ∈ 0 , 1 ∴ x sin ( π x ) = 0 ∴ I = 2 ∫ 0 1 0 d x = 0

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