Answer
$$A = \frac{{5\left( {\root 5 \of {16} - 1} \right)}}{2}$$
Work Step by Step
$$\eqalign{
& f\left( x \right) = {x^{ - 3/5}};\,\,\,\,{\text{Interval }}\left[ {1,4} \right] \cr
& {\text{The area is given by }} \cr
& A = \int_1^4 {{x^{ - 3/5}}} dx \cr
& A = \left[ {\frac{{{x^{2/5}}}}{{2/5}}} \right]_1^4 \cr
& A = \frac{5}{2}\left[ {{x^{2/5}}} \right]_1^4 \cr
& A = \frac{5}{2}\left( {{4^{2/5}} - {1^{2/5}}} \right) \cr
& A = \frac{5}{2}\left( {{4^{2/5}} - {1^{2/5}}} \right) \cr
& A = \frac{{5\left( {\root 5 \of {16} - 1} \right)}}{2} \cr} $$
