MATHEMATICA Lab Project
September 1, 2006
Do MATHEMATICA experiments working out answers to the questions below. When you're done, clean up your
file (delete any cells which are unnecessary), add comments if appropriate,
put a title and your name at the top, print out the notebook and turn it in.
- Consider the definite integral of the function f(x) = 1 + 1/x3.1 on the interval
from a=5 to b=10.
- Use MATHEMATICA to determine approximate values of left-hand, right-hand and midpoint Riemann
sums for the definite integral, taking a few different values for n, say 10, 100,
1000, and 10000.
Use the definitions of the functions LeftSum, RightSum
and MidpointSum from the sample MATHEMATICA session computing Riemann sums
as a model for your work. Also refer to the Getting Started with MATHEMATICA
web page as needed.
- If you wanted to approximate the actual value of the integral to within 3 decimal places using
the midpoint Riemann sum, what value of n would suffice? Try to get close to the smallest value of n
that works.
- Answer the questions from the previous problem for the same function but on the interval from
a=1/2 to b=1.
- Repeat the above with f(x) = sin(x) - sin(2x) + sin(3x) on the interval
from a=-Pi to b=Pi. Can you explain (maybe with a graph) what is going on in this example?