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Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals1 Mark
MCQ
If $\text{g}'(\text{x})=\int\text{x}^\text{x}\log_\text{e}(\text{ex})\text{dx}$ then $\text{g}(\pi)$ equals :
  • A
    $\pi\log_\text{e}\pi$
  • B
    $\pi^\pi\log_\text{e}(\text{e}\pi)$
  • C
    $\pi^\pi\log_\text{e}(\pi)$
  • ✓
    $\pi^\pi$
✓

Answer

Correct option: D.
$\pi^\pi$
$\text{g}\ '(\text{x})=\int\text{x}^{\text{x}}(1+\log{\text{e}^\text{x}})\text{dx}$
$=\int\text{d}(\text{x}^{\text{x}})$
$\text{g'}(\text{x})=\text{x}^{\text{x}}$
$\text{g'}({\pi})={\pi}^{\pi}$

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