The dye dilution method is used to measure cardiac output with $6 \mathrm{mg}$ of dye. The dye concentrations, in $\mathrm{mg} / \mathrm{L}$, are modeled by $c(t)=20 t e^{-0.6 t}, 0 \leqslant t \leqslant 10$, where $t$ is measured in seconds. Find the cardiac output.
6.6