$ M = \frac{\int_1^9 \sqrt{x} \, dx} {9-1} = \left. \frac{2\sqrt{x}}{8} \right|_1^9 = \frac{52}{3 \cdot8} = \frac{13}{6}$
$ f(c) = M $
$ \sqrt{c} = \frac{13}{6}$
$ c = \frac{169}{36}$
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