A) \[\sqrt{x-1}\]
B) \[\sqrt{x+1}\]
C) \[\sqrt{{{x}^{2}}+1}\]
D) \[\frac{x}{\sqrt{1+{{x}^{2}}}}\]
Correct Answer: D
Solution :
Area\[=\int_{x=1}^{b}{f(x)}dx=\sqrt{{{b}^{2}}+1}-\sqrt{2}\] \[=\sqrt{{{b}^{2}}+1}-\sqrt{1+1}\] \[=|\sqrt{{{x}^{2}}+1}|_{1}^{b}\] \[\Rightarrow \] \[f(x)=\frac{d}{dx}(\sqrt{{{x}^{2}}+1})\] \[=\frac{x}{\sqrt{{{x}^{2}}+1}}\]You need to login to perform this action.
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