Answer
$\frac{1444}{225}$
Work Step by Step
Find the values of c guaranteed by the mean value theorem
$\int ^9_4\sqrt x dx= f(x)(9-4)$
$\int ^9_4 \sqrt xdx= 5\sqrt x$, Integrate
$[\frac{2}{3}x^{\frac{3}{2}} ]^9_4= 5\sqrt x$
$ (18-\frac{16}{3})=5\sqrt x$
$\frac{38}{3}= 5\sqrt x$
$\frac{1444}{225}=x$
