Only question I can't do on the assignment
In pharmacokinetics the area under the graph of the drug concentration function with respect to time can be used to determine the total amount of the drug absorbed (the area is actually proportional to the amount of the drug absorbed). The blood alcohol 1concentration after a drink has been consumed can be modelled by
c(t) = 0.02te^(-0.05t)
where t is the time elapsed in minutes after the consumption of the drink and c(t) is the concentration in mg/mL at t. Evaluate the Definite Integral, from 0 to 5, of c(t)dt.
∫te^at dt needs to be done with integration by parts, with
u = t, du = dt
dv = e^at dt, v = 1/a e^at
Do all that and you have
∫0.02te^(-0.05t) dt = -(0.4t+8)e^(-0.05t)
now just plug in the numbers