Chapter 21, Problem 24P

The total mass of a variable density rod is given by

$m={\displaystyle {\int }_0^L\rho \left(x\right)A_c\left(x\right)dx}$

where m = mass, $\rho \left(x\right)$= density, $A_c\left(x\right)$ = cross-sectional area, x = distance along the rod, and L = the total length of the rod. The following data have been measured for a 10-m length rod. Determine the mass in kilograms to the best possible accuracy.

x, m	0	2	3	4	6	8	10
$\rho$, g/cm3	4.00	3.95	3.89	3.80	3.60	3.41	3.30
Ac, cm2	100	103	106	110	120	133	150