Answer
$$A = \frac{{52}}{3}$$
Work Step by Step
$$\eqalign{
& f\left( x \right) = \sqrt x ;\,\,\,\,{\text{Interval }}\left[ {1,9} \right] \cr
& {\text{The area is given by }} \cr
& A = \int_1^9 {\sqrt x } dx \cr
& A = \left[ {\frac{{{x^{3/2}}}}{{3/2}}} \right]_1^9 \cr
& A = \frac{2}{3}\left[ {{x^{3/2}}} \right]_1^9 \cr
& A = \frac{2}{3}\left( {{9^{3/2}} - {1^{3/2}}} \right) \cr
& A = \frac{2}{3}\left( {27 - 1} \right) \cr
& A = \frac{{52}}{3} \cr} $$
