## MA/CS 371 - Lab 5

More Numerical Integration - The Composite Trapezoid Rule (CTR)
Versus The Composite Simpson's Rule (CSR)

### Section 1: Introduction

In this lab you will:
- Write a practical implementation of the CSR
- Compare the convergence behavior of the CSR and the CTR.

If you have not already done so, create a directory for this lab and
copy the lab 5 files into it. If you start off in your home directory you
can do the following:

mkdir ~/cs371/lab5
cd ~/cs371/lab5
cp ~cs371/lab5/* .

and (as always) don't forget to type that last period.
### Section 2: Topics for Lecture

Today in lecture I'm going to discuss the **flops** command which
is used to count the number of "floating-point operations" that MATLAB
performs. Comparing the "flops count" of two different algorithms is
one way of determining which is more efficient.
### Section 3: Today's Function

Today's special guest function is one with some flat spots and some
sharp curves:
x sin(x)
f(x) = sin(e ) - e

This week we are going to estimate the integral of f(x) from -10 to 3
with the Composite Simpson's Rule and compare the results to the
Composite Trapezoid Rule.
First off, I recommend that you plot f(x) on the interval [-10,3] just
to see what it's doing. Make sure to use enough points that you can
see how the function wiggles around towards the upper end of the
interval.

### Section 4: Implementing the Composite Trapezoid Rule

The **trap.m** file given to you for this lab is the one that I
wrote for the previous lab assignment. For this lab, you should
modify **trap.m** in the following ways:
- Approximate
**func(x)** instead of 1-sin(x).
- Integrate from -10 to 3 instead of 0 to pi/2.
- Add another column to your table which shows how many
**flops** are required for each number of partitions.

### Section 5: Implementing the Composite Simpson's Rule

Using your **trap.m** function as a template, make a new file
**simpson.m** which will approximate the integral with the CSR.
(Note: Problem 5.4.1 in the book contains the formula for the CSR.)
Use the same number of intervals as in **trap.m** and format
your output the same way.
*Recall that the CSR requires an even number of intervals
(or an odd number of evaluation points.)* You will need to change
the vector **q** in **simpson.m** to accommodate this.

### Section 6: Submitting Your Work

When you are ready, run
~cs371/submit lab5

to submit your **simpson.m** and **trap.m** files.
This
Week's Questions