question_answer

The value of the integral \[\int_{1/4}^{4}{\left| {{\log }_{4}}x \right|}\,dx\]is

A)  \[\frac{1}{4}{{\log }_{4}}\,\,\left( \frac{{{e}^{9}}}{{{4}^{15}}} \right)\]        

B)  \[\frac{1}{4}{{\log }_{4}}\,\,\left( \frac{{{4}^{15}}}{{{e}^{9}}} \right)\]

C)  \[\frac{1}{2}{{\log }_{4}}\,\,\left( \frac{{{e}^{9}}}{{{4}^{15}}} \right)\]                    

D)  \[\frac{1}{2}{{\log }_{4}}\,\,\left( \frac{{{4}^{15}}}{{{e}^{9}}} \right)\]

E)  None of these