This project is under construction
The due date for project 5 is 1 Mar

General Rules for Maple projects.

1. Your name must appear on all printed pages as Maple input.
2. Assignments must be stabled (not paper clipped).
3. Maple output can be confusing if the worksheet is not executed
from top to bottom. Make sure you to execute the the worksheet
from top to bottom before printing.
4. Some Maple programs use too big font for printing. Be sure the
font size is reasonable.
5. The student version of Maple has a "smartplot", do NOT use this.
6. Include your name in the title of any plot.

Hints: Integration and Numerical Integration in Maple
#A Maple likes to think it can integrate most anything symbolically
and turns answers that will not always look friendly. For example
int(exp(-x^2),x=0..1); returns erf(1) times sqrt pi / 2.
int(sin(x^2),0..Pi); returns a value in terms of the FresnelS function.
#B As always one can force Maple to printf a numerical answer by
evalf. So evalf(int(f(x),x=a..b)) usually causes maple to find the
exact answer and then turn the answer into a number.
#C Forcing numerical integration, evalf(Int(f(x),x=a..b)) will use
numerical integration to compute the integral. Note Int and not int.
#D Computing anti-derivatives. To find F(x) st F'(x) is f(x), use
int(f(x),x) -- with no limits.

Project 5. (This project can be done individually or in groups of 2)
If you do it as a group, I need each member of a group to make a statement
saying roughly what percentage each person contributed. (If everyone
agrees on the relative percentages, this can be one page with everyones
signature.)

Making Maple output look nicer:
Try some of these:
Diff(x^3,x) = diff(x^3,x);  or 'diff(x^3,x)' = diff(x^3,x); 
Limit(f(x),x=a) = L; or 'limit(f(x),x=a)' = L;
Sum(i,i=1..4) = sum(i,i=1..4); or 'sum(i,i=1..4)' = sum(i,i=1..4);
Int(x^3,x=1..3) = int(x^3,x=1..3); or 'int(x^3,x=1..3)' = int(x^3,x=1..3);

Problems:
#1 Acquire the Maple worksheep that defines LeftSum and RightSum. Netscape
users can go to http://www.math.fsu.edu/~bellenot/class/f98/cal1/leftsum.mws
while taylor/ulab folks can get by typing 
cp ~bellenot/cal1/leftsum.mws .
and start your project using this worksheet. Be see to change the name
and execute all the lines.
#2 Use "int" to compute the integral of x^3 from 1 to 3. Use "evalf(Int"
to numerically compute this number. (Note int vs Int).
#3 Compute the LeftSum and RightSum for the integral in #2 for n=100,
1000, and 10000.
#4 For the same integral in #2, figure out the n so that 
RightSum(1,3,n)-LeftSum(1,3,n) <= 0.01 but 
RightSum(1,3,n-1)-LeftSum(1,3,n-1) >  0.01 by
using the error estimate like in Example 2 page 148.
and check your answer by computing the differences. 
#5 Compare evalf(int and evalf(Int for the function e^(-x^2) from a=0 to b=1
also have maple do int(f(x),x=a..b).
#6 Find F(x) so that F'(x) = x^5+x^4+x^3+x^2+x+1 using int.
For 7-10 Plot f(x) and int((f(t),t=0..x) on the same graph for the given f(x)
and range. (There is a kind of error you may have which the note below
can fix. Eariler versions of maple had this problem. )
#7 f(x) = x^3, x=0..4
#8 f(x) = cos(x), x=0..2*Pi
#9 f(x) = e^x, x=0..2
#10 f(x) is piecewise defined for x in [0,2], f(x) = x; for x in [2,4]
f(x) = 2 and for x in [4,6], f(x) = 6 - x.

note: One way to do this is 
plot([f(x),int(f(t),t=0..x)], ...
another is to define g:=x->int(f(t),t=0..x) and
plot([f(x),g(x)], ...
On some versions of Maple this last version can give an error (something
about bad limits) if so try
plot([f(x),'g(x)'], ...