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MHT CET202416 May 2024Morning ShiftMathematicsIndefinite IntegrationActual

If f (x)= ^2 x 1+ ^x , then ( f (x)+ f (-x)) d x is equal to

Options

  1. Ax 2 - x 2 + c , (where c is a constant of integration)
  2. B1 2 x- 2 x 4 + c , (where c is a constant of integration)
  3. Cx 2 - x 2 + c , (where c is a constant of integration)
  4. D1 1+ ^x + ^2 x 2 + c , (where c is a constant of integration)

Correct answer

B. 1 2 x- 2 x 4 + c , (where c is a constant of integration)

Step-by-step solution

aligned & ( f (x)+ f (-x)) d x & = [ ^2 x 1+ ^x + ^2(- x) 1+ ^ -x ] d x & = ( ^2 x 1+ ^x + ^x ^2 x ^x+1 ) d x aligned aligned & = ^2 x ( 1+ ^x 1+ ^x ) d x & = ^2 x ~d x & = ( 1- 2 x 2 ) d x & = x 2 - 1 2 2 x 2 +c= x 2 - 2 x 4 +c aligned

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