University of Rhode Island
1. Find the following integrals:
(2 cos( t ) - 1/ t2
+ e3t + t2
+ 2) dt,
(b) Find the following
integral by substitution. Show your work step-by-step
2x /(x2 + 3) dx.
2. Find the average value of the function f(x) = x2 + 4x between
x = 0 and x = 6.
3. Find the average value
of the function f(x) = x + sin(x) between x = 0 and x = 2.
x/( x2 + 4) dx by using substitution.
5. Let C(t) denote the concentration of a drug in blood stream, measured
in mg/cm3 , t hours after an injection. Using the graph of C(t) below estimate the average concentration of a drug in blood stream over the 12-hour period following the injection. Give units with your
6. The relative rate of growth P'(t)/P(t) of a population
P(t) over a 50-year period is given below.
By what factor has the population increased during the period ?