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99 Percentile Qs Bank for JEE MainMathematicsDefinite Integration

∫ - 1 0 d x x 2   +   x   +   2 is equal to

Options

  1. A4 7 tan − 1 1 7
  2. Bπ 2
  3. C2 7 tan − 1 2 7
  4. D- π

Correct answer

A. 4 7 tan − 1 1 7

Step-by-step solution

Let I = ∫ - 1 0 d x x 2   +   x   +   2 =   ∫ - 1 0 d x x + 1 2 2 + 2 - 1 4 =   ∫ - 1 0 d x x + 1 2 2 + 7 2 2 = 1 7 2 tan - 1 x + 1 2 7 2 - 1 0 = 2 7 tan - 1 2 x + 1 7 - 1 0 = 2 7 tan − 1 1 7 − tan − 1 − 1 7 = 2 7 × 2 tan − 1 1 7 =   4 7 tan - 1 1 7

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