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JEE Main202228 Jun 2022Morning ShiftMathematicsDefinite IntegrationActual

Let t denote the greatest integer less than or equal to t . Then, the value of the integral ∫ 0 1 - 8 x 2 + 6 x - 1 d x is equal to

Options

  1. A- 1
  2. B- 5 4
  3. C17 - 13 8
  4. D17 - 16 8

Correct answer

C. 17 - 13 8

Step-by-step solution

The graph of y = - 8 x 2 + 6 x - 1 will be as shown Now ∫ 0 1 - 8 x 2 + 6 x - 1 d x = ∫ 0 1 4 - 1 d x + ∫ 1 4 1 2 0 d x + ∫ 1 2 3 4 - 1 d x + ∫ 3 4 3 + 17 8 - 2 d x + ∫ 3 + 17 8 1 - 3 d x = - x 0 1 4 + 0 - x 1 2 3 4 + - 2 x 3 4 3 + 17 8 - 3 x 3 + 17 8 1 = - 1 4 - 0 - 3 4 - 1 2 - 2 3 + 17 8 - 3 4 - 3 1 - 3 + 17 8 = - 1 4 - 1 4 + - 6 - 2 17 8 + 3 2 - 3 + 9 + 3 17 8 = 17 - 13 8

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