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KCET2014MathematicsContinuity and Differentiability

( 2 x ( ² x+2 ² x . d x= )

Options

  1. A( (1+ ² x )+C )
  2. B( (1+ ² x )+C )
  3. C( - (1+ ² x )+C )
  4. D( - (1+ ² x )+C )

Correct answer

D. ( - (1+ ² x )+C )

Step-by-step solution

Given that, I= 2 x ² x+2 ² x d x Since, ² x=1- ² x . So, = 2 x d x 1+ ² x Let 1+ ² x=t . So, -2 x x d x=d t 2 x d x=-d t - d t t =- t+c=- (1+ ² x )+c

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