A) \[\sqrt{x-1}\]
B) \[\sqrt{x+1}\]
C) \[\sqrt{{{x}^{2}}+1}\]
D) \[\frac{x}{\sqrt{1+{{x}^{2}}}}\]
Correct Answer: D
Solution :
[d] Given \[\int\limits_{1}^{b}{f(x)dx=\sqrt{{{b}^{2}}+1}}-\sqrt{2}\] Differentiate with respect to b \[f(b)=\frac{b}{\sqrt{{{b}^{2}}+1}}\Rightarrow f(x)=\frac{x}{\sqrt{{{x}^{2}}+1}}\]
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