MAT 202 Notes, Spring 2011
American University of Science and Technology · Calculus II · 2 pages · Ms. Hiba Othman
More MAT 202 files
- Useful File Notes Trigo · Spring 2019NotesView
- Notes · Fall 2011NotesView
- Useful File Trigonometric Formulas · Fall 2014FileView
- Exam 1 Summary · Fall 2014ExamView
- Final · Fall 2013Final examView
- Exam 2 · Fall 2013ExamView
- Exam 1 With Solution · Fall 2013Exam · with solutionView
- Useful File · Spring 2011FileView
Show the text of this notes
SUMMARY - EXAM I- MAT 102/202 PREPARED BY: HIBA OTHMAN
Method
When to Use
Formula
Volumes by
slicing
When the cross section is specified
or
, where
or
when the cross-
section is a circle (R: radius, D: diameter)
or
when the cross-section is
a square (s: side or base, d: diagonal)
or
when the cross-
section is an equilateral triangle (b: side or
base, h: height)
Volumes by
Disks
When two functions are revolved about an axis to
constitute one region running between both
functions
(the disk method gives a solid with no empty space
inside)
to get the
volume about the x-axis
to get the
volume about the y-axis
Volumes by
Washers
When two functions are revolved about an axis and
the volume between them is required (the washer
method gives a solid with some empty space
inside)
Note: Rather than drawing to determine which of
the functions is above the second, we use absolute
value.
to get the
volume about the x-axis
to get the
volume about the y-axis
Volumes by
Cylindrical
Shell
When two functions are revolved about an axis and
there are points of intersection between the graphs
of the functions and the axis.
to get the
volume about the y-axis
SUMMARY - EXAM I- MAT 102/202 PREPARED BY: HIBA OTHMAN
Note: Rather than drawing to determine which of
the functions is above the second, we use absolute
value.
to get the
volume about the x-axis
to get
the volume about the line x=k
to get
the volume about the y=k
Length
To calculate the length of functions
when
when
when parametric
equations are given