A) \[{{I}_{1}}>{{I}_{2}}\]
B) \[{{I}_{2}}>{{I}_{1}}\]
C) \[{{I}_{1}}={{I}_{2}}\]
D) \[{{I}_{1}}>2{{I}_{2}}\]
Correct Answer: B
Solution :
We have, \[(1+{{x}^{2}})>{{x}^{2}},\forall x\]; \[\sqrt{1+{{x}^{2}}}>x,\forall \,x\in (1,\,2)\] Þ \[\frac{1}{\sqrt{1+{{x}^{2}}}}<\frac{1}{x},\,\,\forall x\in (1,\,2)\]Þ \[\int_{1}^{2}{\frac{dx}{\sqrt{1+{{x}^{2}}}}<\int_{1}^{\,2}{\frac{dx}{x}}}\] Þ \[{{I}_{1}}<{{I}_{2}}\]Þ \[{{I}_{2}}>{{I}_{1}}\].
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