x2 t06 02 cylindrical shells

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Volumes By Cylindrical Shells

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Volumes By Cylindrical Shells

y

x

xfy

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Volumes By Cylindrical Shells

y

x

xfy

a b

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Volumes By Cylindrical Shells

y

x

xfy

a x b

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Volumes By Cylindrical Shells

y

x

xfy

a x b

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Volumes By Cylindrical Shells

y

x

xfy

a x b

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Volumes By Cylindrical Shells

y

x

xfy

a xx

b

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Volumes By Cylindrical Shells

y

x

xfy

a x

y

xb

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Volumes By Cylindrical Shells

y

x

xfy

a x

y

x

xf

b

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Volumes By Cylindrical Shells

y

x

xfy

a x

y

x

xf

x2b

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Volumes By Cylindrical Shells

y

x

xfy

a x

y

x

xf

xfxxA 2

x2b

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Volumes By Cylindrical Shells

y

x

xfy

a x

y

x

xf

xfxxA 2

xxfxV 2

x2b

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Volumes By Cylindrical Shells

y

x

xfy

a x

y

x

xf

xfxxA 2

xxfxV 2

b

axx

xxfxV 2lim0

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Volumes By Cylindrical Shells

y

x

xfy

a x

y

x

xf

xfxxA 2

xxfxV 2

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a

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axis about the rotated is axis the

and 4between area when thegenerated volume theFind e.g. 2

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axis about the rotated is axis the

and 4between area when thegenerated volume theFind e.g. 2

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axis about the rotated is axis the

and 4between area when thegenerated volume theFind e.g. 2

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y

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axis about the rotated is axis the

and 4between area when thegenerated volume theFind e.g. 2

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y

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axis about the rotated is axis the

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y

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axis about the rotated is axis the

and 4between area when thegenerated volume theFind e.g. 2

xx

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y

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axis about the rotated is axis the

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xx

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y

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4 yx

axis about the rotated is axis the

and 4between area when thegenerated volume theFind e.g. 2

xx

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y

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axis about the rotated is axis the

and 4between area when thegenerated volume theFind e.g. 2

xx

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y

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1

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axis about the rotated is axis the

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xx

xyi

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y

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1

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axis about the rotated is axis the

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y

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1

422 yyyA

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axis about the rotated is axis the

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y

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axis about the rotated is axis the

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semi-circle function odd even odd

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semi-circle function odd even odd

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32units32

2

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Exercise 3B; 3, 4, 6, 8

Exercise 3C;1, 3, 9, 12, 20

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semi-circle function odd even odd

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32units32