The total mass of a variable density rod is given by

$m={\displaystyle \underset{0}{\overset{L}{}}}(x)A_c(x)dx$

where $m$ is mass, $(x)$ is density, $A_c(x)$ is cross$-$sectional area, $x$ is distance along the rod, and

$L$ is the total length of the rod. The following data have been measured for a $20-m$ length rod.

Determine the mass in grams to the best possible accuracy.