Due: February 25th, 2015,
At the beginning of class!
MATH 1220 Assignment 3
Name:
Student #:
Assignment 3
1. Compute the following integrals.
(a)
ex tan3 (ex ) dx
(b)
(4x2 5)1/2 dx
(c)
arctan( x) dx
Page 1
Due: February 25th, 2015,
At the beginning of cla

MATH 1220 Lesson 9 February 4th, 2015
Integration by Parts
Textbook Reference: Section 7.1
Textbook Exercises: Section 7.1 # 5,13,15,21,27,29,33,35,37,45,57
Consider two functions f (:r) and g(:r). We can use the product rule to ﬁnd a very convenient.
for

MATH 1220 Lesson 13 February 25th, 2015
Strategies for Integration
Textbook Reference: Section 7.5
Textbook Exercises: Section 7.5 # 1’77 every 2nd odd number.
Suggestion of Procedure for Computing an IntegraI
I. Simplify the integrand if possible. ., ‘ ‘

MATH 1220 Lesson 10 February 16th, 2015
Trigonometric Integrals
Textbook Reference: Section 7.2
Textbook Exercises: Section 7.2 # 3,5,7,21,23,29,33,41,47,55—61 (odd)
There are common tricks to integrate functions consisting of trigonometric functions rais

MATH 1220 Lesson 12 ' February 23rd, 2015
Integration by Partial Fractions
Textbook Reference: Section 7.4
Textbook Exercises: Section 7.4_ #1 11,17,23,25,31,37,39,43,47,51
There are convenient expansions we can use to integrate rational functions (functi

MATH 1220 Lesson 18
March 18th, 2015
Sequences and Series
Textbook Reference: Sections 11.1 and 11.2
Textbook Exercises: Section 11.1 # 5,7,13,17,19,25,27,33,51,53
Section 11.2 # 3,9,13,15,19,23,27,31,35,39,43
Sequence
A list of numbers written in a denit

MATH 1220 Lesson 11 . _ February 18th, 2015
Trigonometric Substitutions
Textbook Reference: Section 7.3
Textbook Exercises: Section 7.3 # 3,7,13,17,21,?933
We know that
/ «11—? d3: = ar’csin(x) + C
There is another way to obtain this answer: try solving

MATH 1220 Lesson 19
March 18th, 2015
Integral and Comparison Tests
Textbook Reference: Sections 11.3 and 11.4
Textbook Exercises: Section 11.3 # 5,7,11,13,19,21,27
Section 11.4 # 5,9,15,19,23,29,35
We can link the convergence of a series
an where an is a

MATH 1220 Test 1 Review
February 2nd, 2015
Test 1 Review
Textbook Reference: Section 5.1 to 5.5, 6.1 to 6.3, 10.4 and Appendix E
Sigma Notation
Let m, n be two integers such that m n and am , am+1 , , an1 , an be real numbers. Then,
the sum of all those n

_ ' Due: January 12th, 2Ol57
MATH 1220 Week 1 \ I At the beginning of class!
N.- '.3\STW\S , ‘1
MY , I 40
Student #:
Assignmc mi; 1
1. Write the following in sigma notation. You do n it need to evaluate the sums.
(a)1—1'+1-—1+1—1+1;1+1—‘1
‘0 a 41}

MATH 1220 Test 2 Review
March 16th, 2015
Test 2 Review
Textbook Reference: Sections 6.4, 6.5, 7.1 to 7.5, 7.7 and 7.8
Work
A force acting on a body is said to do work if there is a displacement of the point of application
in the direction of the force. If

Due: January 19th, 2015,
MATH 1220 Week 2 At the beginning of Class!
Name: .MV.
Student #:
Assignment 2
1. Compute the following integrals and derivatives. n ‘
~ Av :37 M=SQCXOD<
(a) [seCthanmdm LL :TUUX, Gui : 39A, 4
&x
ﬂaw: UL #C,
1
Z
Z— - : 3+

Math 1220
Midterm Examination 2
4:30-6:20, March 16th, 2015
Student. #: _ _
Do not open this booklet until instructed to do so.
This examination has 5 problems worth a total of points.
It consists of 9 pages, including this one. Make sure your exam co

MATH 1220 Lesson 15
March 4th, 2015
Improper Integrals
Textbook Reference: Section 7.8
Textbook Exercises: Section 7.8 # 7,11,15,19,23,27,31,49,67
Improper Integral
A denite integral of a function f is called an improper integral if either
I) [Innite Inte

MATH 1220 Lesson 14
March 2nd, 2015
Approximate Integration
Textbook Reference: Section 7.7
Textbook Exercises: Section 7.7 # 7,11,15,19,31,39,43,45,47
2 situations in which we cannot compute a denite integral exactly
In many cases, it is not possible to

MATH 1220 Lesson 7
January 26th, 2015
Volumes by Cylindrical Shells
Textbook Reference: Section 6.3
Textbook Exercises: Section 6.3 # 5,9,13,15,17,27,37,39
Consider the volume of revolution obtained by revolving around the y-axis the region of the rst
qua

Due: Wednesday March 25th, 2015,
At the beginning of class!
MATH 1220 Assignment 4
Name:
Student #:
Assignment 4
1. Find a formula for the n-th term of the sequence given by
5 8 11 14 17 20
, , , ,
,
.
1 2 6 24 120 720
2. Determine whether the sequence an

Due: Wednesday April 8th, 2015,
At the beginning of class!
MATH 1220 Assignment 5
Name:
Student #:
Assignment 5
1. In each case, nd the interval of convergence of the given power series:
(a)
n=0
(b)
n=0
1 3 5 (2n + 1) n
x
n!
(1)n 4n n
x
n ln n
Page 1
Due:

MATH 1220 Lesson 17
March 11th, 2015
Dierential Equations
Textbook Reference: Sections 9.1 and 9.3
Textbook Exercises: Section 9.1 # 1,3,5,7,13
Section 9.3 # 7,11,15,19,21,35,39,45,47
Dierential Equation
A dierential equation is an equation which contains

MATH 1220 Lesson 8
January 28th, 2015
Other Applications of Integrals:
Work and Average Value
Textbook Reference: Sections 6.4 and 6.5
Textbook Exercises: Section 6.4 # 5,7,13,15,17,19,21
Section 6.5 # 3,7,9,13,15,17
Work
A force acting on a body is said

MATH 1220 Lesson 22
March 30th, 2015
Power Series
Textbook Reference: Sections 11.8 and 11.9
Textbook Exercises: Section 11.8 # 7,11,15,19,23,27,31
Section 11.9 # 5,9,13,15,25,27,29
Consider the series
x x2 x3 x4
+
+
+
+ .
2
4
8
16
where x is a number whi

MATH 1220 Lesson 23
April 1st, 2015
Taylor and Maclaurin Series
Textbook Reference: Sections 11.10 and 11.11
Textbook Exercises: Section 11.10 # 5,15,17,33,35,47,51,63
Section 11.11 # 5,9,15,19,21,25
Consider a function f (x) with a power series expansion

Due: Wednesch April 8th, 2015,
MATH 1220 Assignment 5 At the beginning of class!
Name: 4 ;
Student #:
Assignment 5
1. In each case, nd the interval of convergence of the given power series:
(3)21-3-5~-l(2n+1)mn
71.
12:0 .
' - (-B-S'~ (J

MATH 1220 Lesson 1
January 5th, 2015
Areas and Sums
Textbook Reference: Section 5.1 and Appendix E
Textbook Exercises: Section 5.1 # 3,5,11,15
Appendix E # 5,9,13,15,19,23,31,35
Distance from Velocity
Consider a particle moving on a straight line. Assume

MATH 1220 Lesson 2
January 7th, 2015
Denite Integral
Textbook Reference: Section 5.2
Textbook Exercises: Section 5.2 # 5,9,17,19,23,25,35,37,39,53,55,57,59
The Denite Integral
Consider a function f dened on an interval [a, b]. Divide the interval into n s

MATH 1220 Lesson 4
January 14th, 2015
Integration by Substitution
Textbook Reference: Sections 5.5
Textbook Exercises: Section 5.5 # 1 73 every 2nd odd number
Integrals are not always easy to compute. For example, we know that
5x 3 dx?
how could we comput

MATH 1220 Lesson 6
January 21st, 2015
Volumes by Integrating
Areas of Cross-Sections
Textbook Reference: Section 6.2
Textbook Exercises: Section 6.2 # 1,5,9,11,17,21,25,37,49,51,55
Integrating Cross-Sections
The denite integral can be used to nd the volum