Math 155-004, Quiz 13
May 5, 2009
NAME:
Instructions: You may use calculators. Work that is erased or crossed out will not be graded.
1. (2 points) Find the left-hand estimate to the definite integral of the function et from t = 0 to t = 1. Use
n = 2.
2. (4 √points) Evaluate the following integrals:
R π
(a) 0 3t sin(t2 )dt
(b)
R∞
1
1
x2 dx
3. (2 points) Find the area under the graph of the curve g(x) = xe2x for 1 ≤ x ≤ 2 (use integration by
parts).
4. (2 points) The population p(t) of bunny rabbits in Ingersoll Meadow follows the differential equation
dp
= 4 + 2 sin(3t),
dt
and the population at time t = 0 is 100. (a) Express the total change in the population between times t = 0
and t = π3 as a definite integral. (b) Evaluate the definite integral.
Extra Credit:
The basic model used to analyze the dynamics of infectious disease is a system of
.