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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 30 "Lesson 4  Volumes using Sh
ells" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 93 "H
ere are the solids of revolution for the examples which were worked in
 class using shells.  " }{TEXT 256 76 "Press the ENTER key on each lin
e of command in order to execute the command." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 
257 0 "" }{TEXT 258 9 "Example 1" }{TEXT 259 0 "" }{TEXT -1 4 "    " }
{TEXT 260 1 "y" }{TEXT -1 5 " =   " }{XPPEDIT 18 0 "1/x;" "6#*&\"\"\"
\"\"\"%\"xG!\"\"" }{TEXT -1 2 ", " }{TEXT 262 1 "x" }{TEXT -1 6 " = 1,
 " }{TEXT 263 1 "x" }{TEXT -1 6 " = 3, " }{TEXT 264 1 "y" }{TEXT -1 
25 " = 0 ; revolve about the " }{TEXT 272 1 "y" }{TEXT -1 5 "-axis" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 81 "tubeplot([0,0,z], z=1/3..1, radius=1/z, tubepoints=40, color=pin
k): solid11 := %:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "tubepl
ot([0,0,z], z=0..1, radius=1, tubepoints=40, color=pink): solid12 := %
:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "tubeplot([0,0,z], z=0.
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "display(solid11,solid12,solid13);" 
}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 43 
"View of the solid looking upwards from the " }{TEXT 265 1 "x" }{TEXT 
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0 "" {MPLTEXT 1 0 103 "tubeplot([0,0,z], z=1/3..1, radius=1/z, tubepoi
nts=40, color=pink, orientation=[38,140]): solid14 := %:" }}}{EXCHG 
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 radius=3, tubepoints=40, color=pink, orientation=[38,140]): solid16 :
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id15,solid16);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }{TEXT 266 0 "" }{TEXT 267 9 "Example 2" }{TEXT 
268 0 "" }{TEXT -1 3 "   " }{XPPEDIT 18 0 "y = sqrt(x);" "6#/%\"yG-%%s
qrtG6#%\"xG" }{TEXT -1 4 " ,  " }{TEXT 269 1 "y" }{TEXT -1 8 " = 0 ,  \+
" }{TEXT 270 1 "x" }{TEXT -1 25 " = 9 ; revolve about the " }{TEXT 
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{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
{TEXT 273 78 "See Example 3 of Lesson 3 using washers.  The solid of r
evolution is the same." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 
274 0 "" }{TEXT 275 9 "Example 3" }{TEXT 276 0 "" }{TEXT -1 3 "   " }
{XPPEDIT 18 0 "x^2 = 4*y;" "6#/*$%\"xG\"\"#*&\"\"%\"\"\"%\"yGF)" }
{TEXT -1 5 "  ,  " }{TEXT 277 1 "y" }{TEXT -1 27 " = 2  ;  revolve abo
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{TEXT -1 72 "View of the solid cut in half looking from the origin dow
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{TEXT 279 0 "" }{TEXT 280 9 "Example 4" }{TEXT 281 0 "" }{TEXT -1 3 " \+
  " }{XPPEDIT 18 0 "y = x^2-5*x;" "6#/%\"yG,&*$%\"xG\"\"#\"\"\"*&\"\"&
F)F'F)!\"\"" }{TEXT -1 5 "  ,  " }{TEXT 282 1 "y" }{TEXT -1 27 " = 0  \+
;  revolve about the " }{TEXT 283 1 "y" }{TEXT -1 5 "-axis" }}{PARA 0 
"" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 96 "tub
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tubeplot([0,0,z], z=-25/4..0, radius=-sqrt(z+25/4)+5/2, tubepoints=40,
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25 "display(solid41,solid42);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 57 "View of the solid from the bottom loo
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{TEXT -1 0 "" }{TEXT 285 0 "" }{TEXT 286 9 "Example 5" }{TEXT 287 0 "
" }{TEXT -1 3 "   " }{XPPEDIT 18 0 "x = y^2;" "6#/%\"xG*$%\"yG\"\"#" }
{TEXT -1 5 "  ,  " }{TEXT 288 1 "x" }{TEXT -1 3 " = " }{TEXT 289 1 "y
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}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 44 "
View of the solid looking down the positive " }{TEXT 291 1 "x" }{TEXT 
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View of the solid cut in half looking down the positive " }{TEXT 293 
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