Answer
$63 \ \text{grams}$
Work Step by Step
We are given that a thin bar with a variable density let us say $ \rho=3+2 \sqrt x$ on the interval $0 \leq x \leq 9$
Thus, the mass can be calculated as:
$Mass, M=\int_0^9 3+2 \sqrt x \ dx$
or, $=[3x+\dfrac{4x^{3/2}}{3}]_0^9$
or, $=[3(9-0)+\dfrac{4(9)^{3/2}}{3}-0]_0^9$
or, $=27+36$
or, $=63 \ \text{grams}$
