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NDA2012MathematicsDefinite IntegrationActual

What is ₀^1 ⁻¹ x 1+x^2 d x equal to?

Options

  1. A4
  2. B8
  3. C^2 8
  4. D^2 32

Correct answer

D. ^2 32

Step-by-step solution

aligned & ₀^1 ⁻¹ x 1+x^2 d x & Put ⁻¹ x=t & 1 1+x^2 d x=d t & x=0, t=0 & / 4 & ₀^ / 4 t d t x=1, t= / 4 & t^2 2 ₀^ / 4 & 1 2 [ ( 4 )^2-(0)^2 ] 1 2 ( 16 )^2= ^2 32 . aligned

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