More arc length and numerical estimates
M ath 202
In completing this worksheet, you will calculate the arc length of several more curves both exactly, using
formulas from your table of integrals, and approximately, using several new numerical methods.
Par
MATH 202: Calculus II
Hood College, Spring 2013
Partial Fractions Practice Problems
Problem 1. Express as a partial fraction:
1
x(x + 3)
Problem 2. Express as a partial fraction1:
x2
6
+ 2x 8
1Note that in cases like this one, you may have to factor the d
Find the center of mass of this system. The masses are in grams, and the distances are in centimeters.
Mass (grams)
15
10
20
x-coordinate (centimeters)
20
35
50
A stiff horizontal rod of negligible mass has 1-ounce fishing weights suspended at 6, 14, and
Algebraic substitutions : first example
Calculate
1 + .
1. What does the indefinite integral notation mean? (What is it asking us to find?)
2. Let = 1 + . We then have
=
= _.
3. Rewrite 1 + entirely in terms of and :
1 + = _.
4. We can now rewrite out
MATH 202: Calculus II
Hood College, Spring 2013
Integration by Parts Worksheet
1.1. We Can Do It! Warm-ups. .
So far, we have learned a few basic integrals:
Type of Integral
Example
Indenite Integral
x3 dx
Power Functions
x2 + 3x + 1dx
1
dx
x
e2x + 3x dx
Trigonometric Substitutions worksheet
M ath 202
1. In the inverse lab, you found that
_.
Letsgetthisformulabyadifferenttechnique,usingsubstitution in a new way.
2. Set
We then have
3. Assume that
_.
. Use a trigonometric identity to simplify
_.
4. Rewrite
1/09
M A T H 202 C A L C U L U S I I
W O R K S H E E T : C A L C U L US S K I L L S R E V I E W
Instructions: Work these problems in groups.
1. F i n d t h e d e r i v a t i v es of e a c h of t h e f ol l ow i n g f u n c t ions :
f (t )
(a)
f (t )
2t 3
F iona Lyons
4 February 2013
Population Models
What is the best way to model changes in population over time? There are several factors to
consider, such as the size of the initial population, if there is a limit that the population can reach,
the rate at
Reliability Theory: How long do things
last?
M ath 202
This worksheet follows Sections 9.1.1 and 9.1.2 of our text closely.
If you go to the store and buy a package of 100-watt light bulbs, you will see on the package a statement
about the average life o
Limiting values and improper integrals
We found using our model that the total lifetime of the light bulbs that fail between days and
where
. Since almost all of the light bulbs have burned out by, say,
seems reasonable that as
gets larger and larger (or
Continuous probability distributions
1.
(This problem comes from Section 9.3.1 of our textbook.) Figure 2 shows the spinner (slightly
modified) from the popular children's game Chutes and Ladders. Its purpose is the select a random
integer from 1 to 6. H
M a t h 202 C a l c u l u s I I
E xam 1
S p r i n g, 2009
Name : _
You may use one sheet of notes and your calculator on this exam. Be sure to show a l l w o r k
and answer all questions completely.
1
from x = 1 to x = 3 using a Left Hand
x
Sum with n = 4
CalculusII:ReviewPacket
Working through the activities in this review packet will help you prepare for our final exam. I
have put the chapters of the text that we discussed in reverse order, since many of the trickiest
concepts came in the later chapters.
F iona Lyons
4 February 2013
Population Models
What is the best way to model changes in population over time? There are several factors to
consider, such as the size of the initial population, if there is a limit that the population can reach,
the rate at
Algebraic substitutions : first example
Calculate
1 + .
1. What does the indefinite integral notation mean? (What is it asking us to find?)
2. Let = 1 + . We then have
=
= _.
3. Rewrite 1 + entirely in terms of and :
1 + = _.
4. We can now rewrite out
Number of trials
Fiona Lyons
Modeling with the normal distribution
In this worksheet, you will explore a probability model for a coin-flipping experiment. The experiment is
flipping a coin 100 times and counting the number of heads. Figure 1 displays the
Seriesofconstants
This worksheet is about three famous infinite series, the harmonic series, the alternating harmonic
series, and the Leibniz series. These series are different from the infinite series that we have studied so
far, since they are right at
Usingatableofintegrals
Name: _
This worksheet refers to POCKET BOOK OF INTEGRALS AND MATHEMATICAL FORMULAS, 4th Edition, by
Ronald J. Tallarida, Chapman and Hall/CRC Press 2008.
You may work with a partner on this activity. Each student should submit a co