# Day 2

```Math 1431
Lecture - Section 14681 MWF 11am – 12 pm SR 117
Dr. Melahat Almus
[email protected]
http://www.math.uh.edu/~almus
Office Hours in 222 Garrison (CASA):
Starting second week
MW 1-2:30pm, F:1-2 pm.
COURSE WEBSITE:
http://www.math.uh.edu/~almus/1432_sp15.html
Visit my website regularly for announcements and course material!
If you email me, mention your course (Math 1432) in the subject line!
1 Policies Read the syllabus!
 Must have a CASA account. Everyone has free access until the
 Purchase the access code from UH Bookstore by 2/1 or else you’ll
lose access to CASA. No make ups for assignments you missed
due to not having access.
 Must attend both lectures and labs.
CLASSROOM BEHAVIOR:
Be here on time (at least 5 minutes before the lecture so that you can get
seated!)
If you have to be late (on occasion!)- enter quietly without disturbing
others.
Pay attention to the lecture. You are here to learn; stay away from
internet and other distractions for 50 minutes!
Don’t use laptops, don’t surf on the internet during lectures.
Cell phones should be in silent mode.
Bring printed blank notes from my website to class for ease of note
taking.
Respect your friends! Do not distract anyone by chatting with
people around you… Be considerate of others in class.
2 Review of Integration – Continued:
Example: Given that f ''  x   6 x  4 , f '  0   5, f 1  2 , find f  2  .
3 Example: Given that f  x  
2x
 t sin  t  dt ,
find the instantaneous rate of change of
1
f  x  at x 

.
4
4 Example: Given that f  x  is a differentiable function and
x
  f  t   6t  dt  cos  x  ,
0

find f '   .
3
5 Section 7.2 – Average Value of a Function
First Mean Value Theorem for Integrals:
If f is continuous on [a, b], then there is at least one number c in
(a, b) for which

b
a
f  x  dx  f  c   b  a 
The number f (c) is called the average (mean) value of f on [a, b].
6 The area of the region under the graph of f is equal to the area of the rectangle
whose height is the average value.
So….
If f is integrable on [a, b], then the average value of f on the interval is:
Average value = f  c  
1
ba
b
 f  x  dx
a
7 Example: Find the average value of the function over the indicated interval and
find the value(s) of x (the value(s) of c) in the interval for which the function
equals its average value:
f  x   3x 2  2
 0 ,2 
8 Example: Find the average value of the function over the given interval :
f  x   4x3  x2
  1 ,1 
9 Example: Find the average value of the function over the indicated interval :
f  x   cos x,
  
  2 , 2 
10 Example: Find the average value of the function
f  t   et  sin  t 
over the
interval :  0 ,  .
11 Example: Find the average value of the function
f  x   x11  sin x
over the
interval : [-4,4].
12 Example: Given that the average value of an even function over [-2,2] is 10, find
2
 f  x  dx .
0
13 Exercise: An object is in rectilinear motion with acceleration a  t   6t  2 , t  0 .
If the initial velocity is 0, find the average speed of this object over the first 2
seconds.
Take practice test 1 and test 1 SOON!
Homework #1 is posted on my website; due in LAB on Monday.
EMCF#1 is posted on my website; due on Sunday.
Check my website regularly for announcements.
www.math.uh.edu/~almus
14 ```