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STD 12 - 7.1 inderfinite integral — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 7.1 inderfinite integral4 Marks
MCQ
If $f'(x) = \frac{1}{x} + x$ and $f(1) = \frac{5}{2}$, then $f(x) = $
  • ✓
    $\log x + \frac{{{x^2}}}{2} + 2$
  • B
    $\log x + \frac{{{x^2}}}{2} + 1$
  • C
    $\log x - \frac{{{x^2}}}{2} + 2$
  • D
    $\log x - \frac{{{x^2}}}{2} + 1$
✓

Answer

Correct option: A.
$\log x + \frac{{{x^2}}}{2} + 2$
a
(a) $f(x) = \int_{}^{} {f'(x)\,dx} = \int_{}^{} {\left( {\frac{1}{x} + x} \right)} \,dx = \log x + \frac{{{x^2}}}{2} + c$
Put $x = 1,$ then $\frac{5}{2} = 0 + \frac{1}{2} + c \Rightarrow c = 2$
Therefore, $f(x) = \log x + \frac{{{x^2}}}{2} + 2.$

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