The amount of mass transported via a pipe over a period of time can be computed as M = t2 t1 Q(t)c(t) dt where M = mass (mg), t1 = the initial time (min), t2 = the final time (min), Q(t) = flow rate (m3 /min), and c(t) = concentration (mg/m3 ). The following functional representations define the temporal variations in flow and concentration: Q(t) = 9 + 5 cos2(0.4t) c(t) = 5e−0.5t + 2e0.15t Determine the mass transported between t1 = 2 and t2 = 8 min with

(a) Romberg integration to a tolerance of 0.1%, obtain an estimate with error O(h6) and calculate εa where appropriate.

b) Determine the mass transported using the three point Gauss-Legendre formula