A) \[\frac{2}{\log 3}.({{3}^{\sqrt{2}}}-1)\]
B) 0
C) \[2.\frac{\sqrt{2}}{\log 3}\]
D) \[\frac{{{3}^{\sqrt{2}}}}{\sqrt{2}}\]
Correct Answer: A
Solution :
Put \[\sqrt{x}=t\]or \[\frac{1}{\sqrt{x}}dx=2\]dt Also, as \[x=0\]to 2 so, \[t=0\]to \[\sqrt{2}\] Therefore, \[\int_{0}^{2}{\frac{{{3}^{\sqrt{x}}}}{\sqrt{x}}\,}dx=2\int_{0}^{\sqrt{2}}{{{3}^{t}}}dt=2\left[ \frac{{{3}^{t}}}{\log 3} \right]_{0}^{\sqrt{2}}\] \[=\frac{2}{\log 3}({{3}^{\sqrt{2}}}-1)\].
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