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JEE Main202117 Mar 2021Morning ShiftMathematicsDefinite IntegrationActual

If [ · ] represents the greatest integer function, then the value of ∫ 0 π 2 x 2 - cos x d x is ___________.

Correct answer

0

Step-by-step solution

I = ∫ 0 π / 2 x 2 + - cos x d x = ∫ 0 1 0   d x + ∫ 1 π / 2   d x + ∫ 0 π / 2 - 1 d x = π 2 - 1 - π 2 = - 1 ⇒ I = 1

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