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JEE Main202229 Jul 2022Evening ShiftMathematicsDefinite IntegrationActual

If t denotes the greatest integer ≤ t , then the value of ∫ 0 1 2 x - 3 x 2 - 5 x + 2 + 1 d x is

Options

  1. A37 + 13 - 4 6
  2. B37 - 13 - 4 6
  3. C- 37 - 13 + 4 6
  4. D- 37 + 13 + 4 6

Correct answer

A. 37 + 13 - 4 6

Step-by-step solution

I = ∫ 0 1 2 x - 3 x 2 - 3 x - 2 x + 2 + 1 d x I = ∫ 0 1 2 x - 3 x - 2 x - 1 d x + ∫ 0 1 1 d x I = ∫ 0 2 3 2 x - 3 x 2 - 5 x + 2 d x + ∫ 2 3 1 2 x + 3 x 2 - 5 x + 2 d x + 1 I = ∫ 0 2 3 - 3 x 2 + 7 x - 2 d x + ∫ 2 3 1 3 x 2 - 3 x + 2 d x + 1 Let I 1 = ∫ 0 2 3 - 3 x 2 + 7 x - 2 d x The graph of y = - 3 x 2 + 7 x - 2 and I 2 = ∫ 2 3 1 3 x 2 - 3 x + 2 d x So I 1 = ∫ 0 α - 2 d x + ∫ α 1 3 - 1 d x + ∫ 1 / 3 β 0 d x + ∫ β 2 3

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