Answer
$450[\dfrac{e-1}{e}] \ \text{grams}$
Work Step by Step
We are given that a thin bar with a variable density let us say $ \rho=150 e^{-x/3}$ on the interval $0 \leq x \leq 3$
Thus, the mass can be calculated as:
$Mass, M=\int_0^3 150 e^{-x/3} \ dx$
or, $=-450 \times [e^{-x/3}]_0^3$
or, $=-450 \times [e^{-3/3}]+450 e^{-0/3}$
or, $=-450[\dfrac{1}{e}-1]$
or, $=450[\dfrac{e-1}{e}] \ \text{grams}$
