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99 Percentile Qs Bank for JEE MainMathematicsDefinite Integration

∫ - 3 2 x + 1 + x + 2 + x - 1 d x is equal to

Options

  1. A31 2
  2. B35 2
  3. C47 2
  4. D39 2

Correct answer

C. 47 2

Step-by-step solution

Let I = ∫ - 3 2 x + 1 + x + 2 + | x - 1   d x Again, let f x = x + 1 + x + 2 + | x - 1 | =   - x + 1 - x + 2 - x - 1 ,     - 3 < x ≤ - 2 - x + 1 + x + 2 - x - 1 ,         - 2 < x ≤ - 1 1 + x + x + 2 - x - 1           - 1 < x ≤ 0 1 + x + x + 2 - x - 1           0 ≤ x < 1 1 + x + x + 2 + x - 1           1 ≤ x < 2 = - 3 x - 2 ,       &

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