Chapter 5.02 Integrals
Feel free to use Wolfram Alpha to help on some of the algebra.
For example, you can type
sum i=1 to n of (3+i*2/n)^2 * 2/n

2
12
14
16 WEP 
18
22
27
28 WEP
------------Part II starts here----------
34
40

QA: Pick one of the following functions:
sin(3x)*sin(2x)
cos(3x)*sin(2x)
cos(3x)*sin(1x)
cos(3x)*cos(2x)
cos(3x)*cos(1x)
Find the integral of that function from x=-pi to pi
hint : graph & use symmetry.
These integrals are related to "Fourier Analysis",
which is at the heart of various technologies
that you might like, such as: DVDs, mp3s,
cell phones, WiFi, and even old fashioned
AM and FM radio.

41 WEP
44 WEP
48
52
56
60

QB (WEP):
i) Do all 3 of the functions in Question A.
What do you notice about all of them?
Then try sin(3x)*sin(1x) ;
do you get the same answer as in Question A?
ii) Now try sin(1x)*sin(1x) or sin(2x)*sin(2x);
How is the result different?
Can you estimate the value using a different kind of symmetry?
Can you generalize to other constants (3, 4, 5, ...) ?
iii) Now try cos(1x)*cos(1x) or cos(2x)*cos(2x);
what can you say now?
iv) Now try sin(0x)*sin(0x) and cos(0x)*cos(0x);
what slightly weird thing happened?
v) Overall, fill in the blanks: if m and n are 
 integers that are >= 0,
 * the integral of sin(m*x)*sin(n*x) from -pi to pi
 	is __ if m=n, and is __ otherwise.
 * the integral of cos(m*x)*cos(n*x) from -pi to pi
 	is __ if m=n, and is __ otherwise.
 * the integral of sin(m*x)*cos(n*x) from -pi to pi
 	is __ if m=n, and is __ otherwise.