# MTH 132

#### University of Rhode Island

Exam #1
Kingston 9/14/2004
**1. **Find the following integrals:

(a)
(2 cos( t ) - 1/ t^{2}
+ e^{3t} + t^{2 }
+ 2) dt,

(b) Find the following
integral by substitution. Show your work step-by-step

2x /(x^{2} + 3) dx.

2. Find the average value of the function f(x) = x^{2} + 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/( x^{2 } + 4) dx by using substitution.

**5. **Let C(t) denote the concentration of a drug in blood stream, measured
in mg/cm^{3 } , 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.

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**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 ?