Chapter 23, Problem 29P

The amount of mass transported via a pipe over a period of time can be computed as

$M={\displaystyle {\int }_{t_1}^{t_2}Q\left(t\right)c\left(t\right)}dt$

where $M=$ mass (mg), $t_1=$ the initial time (min), $t_2=$ the final time (min), $Q\left(t\right)=$ flow rate (m³/min), and $c\left(t\right)=$ concentration (mg/m³). The following functional representations define the temporal variations in flow and concentration,

$Q\left(t\right)=9+4{\cos }^2\left(0.4t\right)$

$c\left(t\right)=5e^{-0.5t}+2e^{0.15t}$

Determine the mass transported between $t_1=2$ and $t_2=8$ min with

(a) Romberg integration to a tolerance of 0.1%, and

(b) The MATLAB quad function.