MTH 132

University of Rhode Island

Exam #1
                                                          Kingston 9/14/2004
1.   Find the following integrals:
(a)    (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.

4.   Find  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 answer.

 
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 ?