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A Review A Review GameGame
•Area between CurvesArea between Curves
•Volumes by SlicingVolumes by Slicing
•Volumes of RevolutionVolumes of RevolutionDisk/WasherDisk/WasherCylindrical ShellsCylindrical Shells
The following will be used throughout this game.
1
0
2
x
y x
y
2
2
y x
xy
3
0
24
y
xy
x
RR11
RR22
RR33
RulesRules: The first : The first team to team to set upset up the the complete, correct complete, correct integral gets a integral gets a pointpoint..
If a team makes If a team makes an incorrect an incorrect guess, they are guess, they are “out” for that “out” for that question. question.
The game begins The game begins with person #1. with person #1. Turns rotate Turns rotate clockwise.clockwise.
Only the person Only the person whose turn it is whose turn it is can write! can write!
And the most And the most important rule….important rule….
Put The Top on Put The Top on the pen when the pen when you’re not you’re not writing!!!writing!!!
ARE YOU ARE YOU READY?READY?
The Game The Game begins with begins with the next slide.the next slide.
Area: R3 with respect to y axis
2
0
(4 2 )y dy
Volume: R3 about y axis using Shell Method
4
0
22
xx dx
Volume: R2 about x axis using Washer Method
24 2
0 2
xx dx
Volume: R3 about x = 4 using Disk Method
2
2
0
4 2y dy
Volume: R1 about y = 2 using Disk Method
4 2
0
2 x dx
Volume: R1 about x axis using Shell Method
22
0
2 ( )y y dy
Volume: R2 about y axis using Washer Method
2
2 2 2
0
(2 ) ( )y y dy
Volume: R1 about x axis using Washer Method
4 22
0
2 x dx
Volume: R1 about y axis using Disk Method
.
. 2
22
0
y dy
Volume: base of R2 with equilateral triangle cross-sections that are perpendicular to the y axis
2
22
0
32
4y y dy
Volume: R2 about y axis using Shell Method
4
0
22
xx x dx
Area: R1 with respect to y axis
22
0
y dy
Volume: with base of R2 with square cross-sections perpendicular to x axis
24
0 2
xx dx
Area: R1 with respect to x axis
4
0
2 x dx
Volume: R3 about x axis using Disk Method
24
0 2
xdx
Volume: R3 about y axis using Washer Method
2
2 2
0
(4) (2 )y dy
Volume: R3 about x axis using Shell Method
2
0
2 4 2y y dy
Area: R3 with respect to x axis
4
0 2
xdx
Volume: with base of R2 with semi-circle cross- sections perpen-dicular to x axis
24
08 2
xx dx
Area: R2 with respect to y axis
2
2
0
2y y dy
Volume: R2 about x axis using Shell Method
2
2
0
2 2y y y dy
Volume: R2 about x = 4 using Shell Method
4
0
2 42
xx x dx
Volume: R1 about y axis using Shell Method
4
0
2 2x x dx
Area: R2 with respect to x axis
4
0 2
xx dx
Volume: R1 about y = 2 using Shell Method
22
0
2 (2 )( )y y dy
GAME GAME OVER!OVER!
