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JEE Main202227 Jun 2022Morning ShiftMathematicsDefinite IntegrationActual

The value of the integral ∫ - 2 2 x 3 + x e x x + 1 d x is equal to

Options

  1. A5 e 2
  2. B3 e - 2
  3. C4
  4. D6

Correct answer

D. 6

Step-by-step solution

Given, f x = x 3 + x e x x + 1 d x and ∫ - 2 2 f x d x = ∫ 0 2 f x + f - x d x = ∫ 0 2 x 3 + x e x x + 1 + - x 3 - x e - x - x + 1 d x = ∫ 0 2 x 3 + x e x x + 1 + x 3 + x e - x x + 1 d x = ∫ 0 2 x 3 + x e x 2 + 1 + x 3 + x e - x 2 + 1 d x I = ∫ 0 2 x 3 + x 1 + e x 2 + e x 2 x 3 + x 1 + e x 2 d x = ∫ 0 2 x 3 + x d x = x 4 4 + x 2 2 0 2 = 4 + 2 = 6

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