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MA/CS 371 - Lab 4

## MA/CS 371 - Lab 4

Numerical Integration - Upper and Lower Sums and the Trapezoid Rule

### Section 1: Introduction

The goal of this lab is to introduce you to:
- Practical implementation of upper and lower sums
- Practical implementation of the trapezoid rule
- formatted output with
**fprintf**

If you have not already done so, create a directory for this lab and
copy the lab 4 files into it. If you start off in your home directory you
can do the following:

mkdir ~/cs371/lab4
cd ~/cs371/lab4
cp ~cs371/lab4/* .

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

This time I'm going to briefly lecture about some of the formatting
options available with MATLAB's **fprintf** command. This command
behaves pretty much the same in MATLAB as it does in C. I'll show you
the overall idea and explain a few of the simpler types.
### Section 3: Upper and Lower Sums

The file **sums.m** is a bare skeleton which you will fill out into
a program which computes approximations to a particular integral via
the upper and lower sums method.
The function we will be approximating will be

pi/2
/
| 1 - sin(x) dx
/
0

The vector **q** in the program indicates the number of
subintervals to use for each approximation. The MATLAB statement
for i=q,

runs through the loop length(q) times, setting i to q(1) the first
time, q(2) the second time, etc.
**Complete the program sums.m and answer the first two questions.**

### Section 4: The Trapezoid Rule

The file **trap.m** is a bare skeleton which you will fill out into
a program which approximates the above function by the trapezoid rule.
**Complete the program trap.m and answer the next two questions.**
### Section 5: Submitting Your Work

When your programs **sums.m** and **trap.m** are ready, run
~cs371/submit lab4

I will accept solutions through 11:59pm Thursday.
As before, I would prefer that you e-mail me the answers to the
problems but there will be a few hard copies in lab.

This
Week's Questions