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JEE Advanced2012MathematicsDefinite IntegrationActual

The value of the integral _ - / 2 ^ / 2 (x²+ +x -x ) x d x is

Options

  1. A0
  2. B² 2 -4
  3. C² 2 +4
  4. D² 2

Correct answer

B. ² 2 -4

Step-by-step solution

_ - / 2 ^ / 2 [x²+ ( +x -x ) ] x d x= _ - / 2 ^ / 2 x² x d x+ _ - / 2 ^ / 2 ( +x -x ) x d x=2 ₀^ / 2 x² x d x+0 [ x² x . is an even function and ( +x -x ) x is an odd function] =2 [x² x+2 x x-2 x ]₀^ / 2 = ² 2 -4

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