x2 t06 02 cylindrical shells (2010)
TRANSCRIPT
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Volumes By Cylindrical Shells
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Volumes By Cylindrical Shellsy
x
xfy
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Volumes By Cylindrical Shellsy
x
xfy
a b
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Volumes By Cylindrical Shellsy
x
xfy
a x b
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Volumes By Cylindrical Shellsy
x
xfy
a x b
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Volumes By Cylindrical Shellsy
x
xfy
a x b
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Volumes By Cylindrical Shellsy
x
xfy
a xx
b
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Volumes By Cylindrical Shellsy
x
xfy
a x
y
xb
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Volumes By Cylindrical Shellsy
x
xfy
a x
y
x
xf
b
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Volumes By Cylindrical Shellsy
x
xfy
a x
y
x
xf
x2b
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Volumes By Cylindrical Shellsy
x
xfy
a x
y
x
xf
xfxxA 2
x2b
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Volumes By Cylindrical Shellsy
x
xfy
a x
y
x
xf
xfxxA 2 xxfxV 2
x2b
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Volumes By Cylindrical Shellsy
x
xfy
a x
y
x
xf
xfxxA 2 xxfxV 2
b
axxxxfxV 2lim
0
x2b
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Volumes By Cylindrical Shellsy
x
xfy
a x
y
x
xf
xfxxA 2 xxfxV 2
b
axxxxfxV 2lim
0
b
a
dxxxf2
x2b
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xxxyi
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xxxyi
x
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and 4between area when thegenerated volume theFind e.g. 2
xxxyi
x
24 xy
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y
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axisabout therotatedis axis the
and 4between area when thegenerated volume theFind e.g. 2
xxxyi
x
24 xy
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y
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axisabout therotatedis axis the
and 4between area when thegenerated volume theFind e.g. 2
xxxyi
x
24 xy
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y
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axisabout therotatedis axis the
and 4between area when thegenerated volume theFind e.g. 2
xxxyi
x
24 xy
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y
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21
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axisabout therotatedis axis the
and 4between area when thegenerated volume theFind e.g. 2
xxxyi
x
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y
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y
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21
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axisabout therotatedis axis the
and 4between area when thegenerated volume theFind e.g. 2
xxxyi
x
24 xy
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y
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21
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21
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and 4between area when thegenerated volume theFind e.g. 2
xxxyi
x
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21
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axisabout therotatedis axis the
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1422 yyyA
21
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axisabout therotatedis axis the
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y
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axisabout therotatedis axis the
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xxxyi
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x
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3units 15
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4line about the
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x
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x
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4
x
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x
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x
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xxxA 4242 2
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x
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x
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xxxA 4242 2
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2
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2
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2
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semi-circle
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xxxxxV
2
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222116
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semi-circle
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2
2
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semi-circle function oddeven odd
2
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0444lim
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222116
2
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semi-circle function oddeven odd
0
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semi-circle function oddeven odd
0
32units32
2
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0444lim
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2
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222116
Exercise 3B; 3, 4, 6, 8
Exercise 3C;1, 3, 9, 12, 20
2
2
22
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2
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22
2
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semi-circle function oddeven odd
0
32units32