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{SECT 0 {PARA 18 "" 0 "" {TEXT 276 26 "AREA AND DEFINITE INTEGRAL" }}
{PARA 4 "" 0 "" {TEXT -1 18 "Calculus I Project" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 0 "" }{TEXT 256 0 "" 
}{TEXT 257 9 "Objective" }}{PARA 0 "" 0 "" {TEXT -1 99 " To explore th
e relationship between the area under a curve and the value of the def
inite integral." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 179 " Using Maple allows the student to easily evaluate a def
inite integral and see the relationship between the area under a curve
 and the value of its definite integral  graphically." }}}{PARA 3 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 3 "
" 0 "" {TEXT -1 0 "" }{TEXT 258 15 "Solved Example:" }}{PARA 0 "" 0 "
" {TEXT -1 15 "  Given f(x) = " }{XPPEDIT 18 0 "x^3-4*x;" "6#,&*$%\"xG
\"\"$\"\"\"*&\"\"%F'F%F'!\"\"" }{TEXT -1 2 ", " }}{PARA 0 "" 0 "" 
{TEXT -1 54 "   a) find the definite integral from x = -2 to x = 2." }
}{PARA 0 "" 0 "" {TEXT -1 24 "   b) plot the function." }}{PARA 0 "" 
0 "" {TEXT -1 74 "   c) find the area between the curve and the x-axis
 from x = -2 to x = 2." }}{PARA 0 "" 0 "" {TEXT -1 33 "   d) determine
 if the values in " }{TEXT 268 1 "a" }{TEXT -1 6 ") and " }{TEXT 269 
1 "c" }{TEXT -1 1 ")" }{TEXT 274 1 " " }{TEXT -1 37 "are equal or uneq
ual and explain why." }}}{PARA 3 "" 0 "" {TEXT -1 0 "" }}{SECT 0 
{PARA 3 "" 0 "" {TEXT -1 0 "" }{TEXT 259 0 "" }{TEXT 260 0 "" }{TEXT 
261 0 "" }{TEXT 262 9 "Solution:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "f:=x->x^3 - 4*x;\n" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%)operatorG%&arrowGF(,&*
$)9$\"\"$\"\"\"F1*&\"\"%F1F/F1!\"\"F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 39 "definiteintegral:=int(f(x),x = -2..2);\n" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%1definiteintegralG\"\"!" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 34 "plot(f(x), x = -2..2, y = -5..5);\n" }}
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9 1 4 2 1.000000 41.000000 35.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 53 "area:=int(f(x),x = -2..0) + abs(int(f(x),x \+
= 0..2));\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%areaG\"\")" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 199 "The definite integral does not equal the area under the \+
curve.  Since the part of the curve below the x-axis is equal to the p
art of the curve above the x-axis, the definite integral will be zero.
   " }}}}{PARA 0 "" 0 "" {TEXT -1 83 "________________________________
___________________________________________________" }}{PARA 257 "" 0 
"" {TEXT -1 0 "" }{TEXT 263 0 "" }}{PARA 258 "" 0 "" {TEXT 264 10 "ASS
IGNMENT" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 3 "" 0 "" 
{TEXT -1 0 "" }{TEXT 265 10 "Problem 1:" }}{PARA 0 "" 0 "" {TEXT -1 
21 "Given f(x) =  sin x, " }}{PARA 0 "" 0 "" {TEXT -1 52 "   a) find t
he definite integral from x = 0 to x = 3" }{XPPEDIT 18 0 "Pi;" "6#%#Pi
G" }{TEXT -1 3 "/2." }}{PARA 0 "" 0 "" {TEXT -1 24 "   b) plot the fun
ction." }}{PARA 0 "" 0 "" {TEXT -1 72 "   c) find the area between the
 curve and the x-axis from x = 0 to x = 3" }{XPPEDIT 18 0 "Pi;" "6#%#P
iG" }{TEXT -1 3 "/2." }}{PARA 0 "" 0 "" {TEXT -1 33 "   d) determine i
f the values in " }{TEXT 270 1 "a" }{TEXT -1 6 ") and " }{TEXT 271 1 "
c" }{TEXT -1 39 ") are equal or unequal and explain why." }}}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 
3 "" 0 "" {TEXT -1 0 "" }{TEXT 266 10 "Problem 2:" }}{PARA 0 "" 0 "" 
{TEXT -1 14 "Given f(x) =  " }{XPPEDIT 18 0 "x^2-1;" "6#,&*$%\"xG\"\"#
\"\"\"F'!\"\"" }{TEXT -1 2 ", " }}{PARA 0 "" 0 "" {TEXT -1 54 "   a) f
ind the definite integral from x = -1 to x = 1." }}{PARA 0 "" 0 "" 
{TEXT -1 24 "   b) plot the function." }}{PARA 0 "" 0 "" {TEXT -1 74 "
   c) find the area between the curve and the x-axis from x = -1 to x \+
= 1." }}{PARA 0 "" 0 "" {TEXT -1 33 "   d) determine if the values in \+
" }{TEXT 272 1 "a" }{TEXT -1 6 ") and " }{TEXT 273 1 "c" }{TEXT -1 39 
") are equal or unequal and explain why." }}}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 3 "" 0 "" {TEXT 
-1 0 "" }{TEXT 267 10 "Problem 3:" }}{PARA 256 "" 0 "" {TEXT -1 130 "E
xplain under what circumstances the area under the curve and the defin
ite integral will be equal and show a worked-out example.  " }}}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 71 "_______________
________________________________________________________" }}{PARA 0 "
" 0 "" {TEXT -1 94 "MSIP Grant #P120A80089-98: \"Three Urban Calculus \+
Reform Programs: Adopting the Best\" 1998-2001" }}}{MARK "8 4 1" 1 }
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