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JEE Main20202 Sep 2020Morning ShiftMathematicsDefinite IntegrationActual

The integral ∫ 0 2 x - 1 - x d x is equal to

Correct answer

0

Step-by-step solution

∫ 0 2 x - 1 - x d x = ∫ 0 1 1 - x - x d x + ∫ 1 2 x - 1 - x d x = ∫ 0 1 2 1 - 2 x d x + ∫ 1 2 1 2 x - 1 d x + ∫ 1 2 d x = x - x 2 0 1 2 + x 2 - x 1 2 1 + x 1 2 = 1 2 - 1 4 - 0 - 0 + 1 - 1 - 1 4 - 1 2 + 2 - 1 = 1 4 + 1 4 + 1 = 3 2 = 1 . 5

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