Comprehension Passage
Direction: For the next two (2) items that follow:
Consider the functions
\({\rm{f}}\left( {\rm{x}} \right) = {\rm{xg}}\left( {\rm{x}} \right){\rm{\;and\;g}}\left( {\rm{x}} \right) = \left[ {\frac{1}{{\rm{x}}}} \right]\)
Where [⋅] is the greatest integer function.
What is \(\mathop \smallint \limits_{\frac{1}{3}}^{\frac{1}{2}} {\rm{g}}\left( {\rm{x}} \right){\rm{dx\;}}\) equal to?
1
\(\frac{1}{6}\)
2
\(\frac{1}{3}\)
3
\(\frac{5}{{18}}\)
4
\(\frac{5}{{36}}\)