The total mass of a rod of variable density can be computed by integrating over the local density at each position $x$ along its length. This can be written as

$m={\displaystyle \underset{0}{\overset{L}{}}}{A}_{c}dx$

where local density $$ and cross sectional area $A_c$ both vary with $x.$ The following data apply to a rod of length $L=10m.$ Evaluate the integral to determine the mass of the rod.

$\backslash$table$[[x(m),0,2,3,4,6,8,10],[(\frac{g}{c}{m}^3),4\mathrm{.}00,3\mathrm{.}95,3\mathrm{.}89,3\mathrm{.}80,3\mathrm{.}60,3\mathrm{.}41,3\mathrm{.}30],[A_c(c{m}^2),100,103,106,110,120,133,150]]$

Suggestion: Note the length units! Also note the uneven spacing in $x.$