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JEE Main2013MathematicsIndefinite IntegrationActual

The integral x d x 2-x^2+ 2-x^2 equals :

Options

  1. A|1+ 2+x^2 |+c
  2. B- |1+ 2-x^2 |+c
  3. C-x |1- 2-x^2 |+c
  4. Dx |1- 2+x^2 |+c

Correct answer

B. - |1+ 2-x^2 |+c

Step-by-step solution

I = x d x 2-x^2+ 2-x^2 aligned & Put t= 2-x^2 , d t d x = 1 2 2-x^2 (-2 x) & aligned & -t d t=x d x & & I = (-t) d t t^2+t =- 1 t+1 d t=- |t+1| &=- | 2-x^2 +1 |+c aligned aligned

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