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JEE Main2002MathematicsDefinite IntegrationActual

_ - ^ 2 x(1+ x) 1+ ^2 x d x is

Options

  1. A^2 4
  2. B^2
  3. Czero
  4. D2

Correct answer

B. ^2

Step-by-step solution

aligned & _ - ^ 2 x(1+ x) 1+ ^2 x d x= _ - ^ 2 x 1+ ^2 x +2 _ - ^ x x 1+ ^2 x & =0+4 ₀^ x x d x 1+ ^2 x I=4 ₀^ ( -x) ( -x) 1+ ^2( -x) & I=4 ₀^ ( -x) x 1+ ^2 x I=4 ₀^ x 1+ ^2 x -4 x x 1+ ^2 x 2 I=4 ₀^ x 1+ ^2 x d x aligned put x=t and solve it.

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