Chapter 5.5, Problem 91E

Dialysis treatment removes urea and other waste products from a patient’s blood by diverting some of the bloodflow externally through a machine called a dialyzer. The rate at which urea is removed from the blood (in mg/min) is often well described by the equation

$u(t)=\frac{r}{V}{C}_0{e}^{-rt/V}$

where r is the rate of flow of blood through the dialyzer (in mL/min), V is the volume of the patient’s blood (in mL), and C₀ is the amount of urea in the blood (in mg) at time t = 0. Evaluate the integral ${\displaystyle {\int }_0^{30}u(t)dt}$ and interpret it.