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AP EAMCET202120 Aug 2021Evening ShiftMathematicsDifferential EquationsActual

If f ' ( x ) = x + 1 x , then f ( x ) =

Options

  1. Ax 2 + log ( x ) + c
  2. Bx 2 2 + log x + c
  3. Cx + log ( x ) + c
  4. Dx 2 + log ( x ) + c

Correct answer

B. x 2 2 + log x + c

Step-by-step solution

f ' x = x + 1 x integrating both sides ∫ f ' ( x ) d x = ∫ x + 1 x d x ∫ f ' ( x ) d x = ∫ x d x + ∫ 1 x d x ⇒ f x = x 2 2 + log x + C

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