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Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals1 Mark
MCQ
If $\text{f}\ '(\text{x})=\text{x}+\frac{1}{\text{x}},$ then value of $f(x)$ is:
  • A
    $\text{x}^2+\log\text{x + c}$
  • ✓
    $\frac{\text{x}^2}{2}+\log\text{x + c}$
  • C
    $\frac{\text{x}}{2}+\log\text{x + c}$
  • D
    None of these
✓

Answer

Correct option: B.
$\frac{\text{x}^2}{2}+\log\text{x + c}$
Given,
$\text{f}(\text{x})=\text{x}+\frac{1}{\text{x}}$
On integrating both sides, we get
$\text{f}(\text{x})=\frac{\text{x}^{2}}{{2}}+\log\text{x + c}$

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