CMSI 186
PROGRAMMING LA B O R A T O R Y
Spring 2008
Program 5: Riemann Integration
With this assignment, we move from arithmetic to calculus — specifically, Riemann integration, a technique
for estimating the area under a curve.
Program to Write
Write a class called math.Riemann that estimates the
area under a cur ve for a user-given range, using the
algorithm described in class. The curve can be one
of a “function library” which you will provide; at a
minimum, your program should support polyno-
mials of arbitrary degree, plus at least three other
functions (examples/ideas on the right).
math.Riemann shall accept three sets of arguments,
identified by the order in which they are given:
•The first argument is a name that uniquely identi-
fies the function to use.
•Zero or more arguments after the function name
supply any additional information needed by the
function (and they thus depend on the function).
•The last two arguments of the command indicate
the range over which the area over the function’s
curve is to be estimated. The range may be given
with either the upper or lower bound first.
As always, math.Riemann should display a helpful
error message if the given arguments are somehow
invalid (e. g., unsupp ort ed functi on names,
incorrect/missing additional information, non-
numeric arguments, etc.).
The output of math.Riemann shall be a table show-
ing one line for each iteration/refinement of your
estimate, starting with a single rectangle (i.e., deltaX
= upperBound – lowerBound) and continuing until the
difference between the previous and succeeding
estimates falls within ±0.01% of each other, after
which the program should stop. The table should
include columns for the iteration number, deltaX,
the estimated area, and the % difference from the
previous estimate.
When invoked with --help as the first argument (i.e.,
java math.Riemann --help), the program should dis-
play a message describing how it should be used,
including a complete list of the functions that it
supports, stating the names to use and the addi-
tional information that they require.
Examples
The following examples illustrate a number of pos-
sibilities which you may implement.
•You must start with a poly function, for polyno-
mials of arbitrary degree. The example below
estimates the area under f(x) = 2x4 – x2 + 9x +
5.2 from x = 1.0 to 3.0:
java math.Riemann poly 2.0 0 –1.0 9.0 5.2 1.0 3.0
•To estimate the area under f(x) = 100 (yes, a hori-
zontal line) from x = –20.5 to 30.75:
java math.Riemann poly 100 30.75 –20.5
•To estimate the area under f(x) = 9x3 + 8x2
+ 7x
+ 6 from x = 0.5 to 1.0:
java math.Riemann poly 9 8 7 6 0.5 1.0
•To estimate the area under f(x) = sin x from x =
0 to 3.141592:
java math.Riemann sin 0 3.141592
•Functions may support coefficients and accom-
panying terms; for example, estimating the area
under f(x) = (2 ln x) + 0.5 from x = 1 to 10 could
look like this:
java math.Riemann ln 2.0 0.5 1 10
•Feel free to create “combo” functions; for exam-
ple, estimating the area under f(x) = cos x – sin x
from x = –3 to 3 could look like this:
java math.Riemann cosMinusSin 3 –3
A Design Note, Extra Work, and a Gotcha
•No unit tests are explicitly required this time
around; if you do implement some tests, use the
test identifier to make the program run them.
•If you finish early, try to implement an optional
--threshold=n argument that changes the program’s
default ±0.01% termination threshold.
•Speaking of termination, there may be other
conditions under which stopping would make
sense. If you suspect you’ve found such a condi-
tion, let me know and we’ll discuss what to do.