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JEE Main202226 Jun 2022Morning ShiftMathematicsDefinite IntegrationActual

Let f x = max x + 1 , x + 2 , … , x + 5 . Then ∫ - 6 0 f x d x is equal to ______.

Correct answer

0

Step-by-step solution

f x = max x + 1 , x + 2 , x + 3 , x + 4 , x + 5 ∫ - 6 0 f x d x = ∫ - 6 - 3 x + 1 d x + ∫ - 3 0 x + 5 d x = - ∫ - 6 - 3 x + 1 d x + ∫ - 3 0 x + 5 d x = - x 2 2 + x - 6 - 3 + x 2 2 + 5 x - 3 0 = - 9 2 - 3 - 18 - 6 + 0 - 9 2 - 15 = - 3 2 - 12 + 21 2 = 21 2 + 21 2 = 21

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