MAT 266 Final: MAT266 Final Study Guide
Arizona State University
MAT 266
Calculus 2
Spring 2018
Final Exam
Prof: Zhu, A.
Exam Guide
Topics Included
Table of Contents
Integration ...................................................................................................................................... 3
Techniques of Integration ............................................................................................................. 4
6.2 Trig integration ................................................................................................................................. 4
6.3 Partial Fractions ............................................................................................................................... 6
6.6 Improper Integrals ........................................................................................................................... 7
Applications of Integration ............................................................................................................ 8
7.1 Areas Between Curves ...................................................................................................................... 8
7.2 Volumes ............................................................................................................................................. 9
7.3 Volumes by Cylindrical Shells ....................................................................................................... 10
7.4 Arc Length....................................................................................................................................... 11
7.6 Applications to Physics and Engineering ..................................................................................... 12
Series............................................................................................................................................. 14
8.1 Sequences ......................................................................................................................................... 14
8.2 Series ................................................................................................................................................ 15
8.4 Convergence tests ........................................................................................................................... 15
8.5 Power Series .................................................................................................................................... 15
8.6 Representing Functions as Power Series ...................................................................................... 15
8.7 Taylor and Maclaurin Series ......................................................................................................... 16
Parametric Equations and Polar Coordinates ............................................................................ 17
9.1 Parametric Curves .......................................................................................................................... 17
9.2 Calculus with Parametric Curves ................................................................................................. 18
9.3 Polar Coordinates ........................................................................................................................... 18
9.4 Areas and Lengths in Polar Coordinates ...................................................................................... 19
Integration
5.5 Substitution Rule
5 Basic Functions:
1. Logarithmic
2. Polynomial
3. Exponential
4. Trig
5. Inverse Trig
General Rule
You use the substitution rule when you have composite functions
Given F(x) = f(x)
This is known as integration by substitution
Choosing “U”
• The function’s derivative should be equal to another term in the integral.
o Usually the highest power
Example:
