{VERSION 5 0 "IBM INTEL NT" "5.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 
0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
257 "" 0 12 0 0 0 0 2 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 258 "" 1 14 0 
0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 259 "" 0 14 0 0 0 0 0 1 0 0 
0 0 0 0 0 1 }{CSTYLE "" -1 260 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 261 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
262 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 263 "" 1 14 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 264 "" 1 12 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 }{CSTYLE "" -1 265 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 266 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
267 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 268 "" 0 14 0 
0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 269 "" 0 1 0 0 0 0 0 2 0 0 0 
0 0 0 0 1 }{CSTYLE "" -1 270 "" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 271 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
272 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 273 "" 0 1 0 0 
0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 274 "" 0 1 0 0 0 0 2 0 0 0 0 0 
0 0 0 1 }{CSTYLE "" -1 275 "" 0 1 0 0 0 0 2 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 276 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
277 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 278 "" 1 14 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 279 "" 0 12 0 0 0 0 0 1 0 0 0 
0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1
" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }1 0 0 0 
8 4 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 
14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 8 2 0 0 0 0 0 0 -1 0 }
{PSTYLE "Heading 3" 4 5 1 {CSTYLE "" -1 -1 "" 1 12 0 0 0 0 1 0 0 0 0 
0 0 0 0 1 }0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 
1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 
0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE 
"" 0 256 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 
-1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 3 257 1 {CSTYLE "" -1 -1 "" 1 
12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }
{PSTYLE "" 3 258 1 {CSTYLE "" -1 -1 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 
1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 259 1 {CSTYLE "" -1 
-1 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 
0 }{PSTYLE "" 3 260 1 {CSTYLE "" -1 -1 "" 1 12 0 0 0 0 0 2 0 0 0 0 0 
0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 261 1 {CSTYLE "" 
-1 -1 "" 1 18 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 
-1 0 }{PSTYLE "" 3 262 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 
0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {PARA 262 "" 0 "" {TEXT 271 0 "" }{TEXT 257 0 "" }{TEXT 272 0 
"" }{TEXT -1 0 "" }{TEXT 257 49 "INTERPRETING THE CONSTANT IN INDEFINI
TE INTEGRALS" }}{PARA 261 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" 
{TEXT 256 19 "Calculus II Project" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT 273 0 "" }}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 0 "
" }{TEXT 257 10 "Objective:" }}{PARA 0 "" 0 "" {TEXT -1 57 "To underst
and the meaning of the constant of integration." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 120 "Using a computer algebra
 system will allow you to quickly integrate a function and then find t
he graph of the integral. " }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 
0 {PARA 5 "" 0 "" {TEXT 275 5 "Solve" }{TEXT -1 0 "" }{TEXT 274 10 "d \+
Example:" }}{PARA 0 "" 0 "" {TEXT -1 67 "a)  Find two different indefi
nite integrals for the function:  f(x)" }{TEXT 278 3 " = " }{XPPEDIT 
18 0 "-2*x^3+6*x;" "6#,&*&\"\"#\"\"\"*$%\"xG\"\"$F&!\"\"*&\"\"'F&F(F&F
&" }}{PARA 0 "" 0 "" {TEXT -1 42 "b)  Plot both integrals on the same \+
graph." }}{PARA 0 "" 0 "" {TEXT -1 66 "c) Write a few sentences compar
ing and contrasting the two graphs." }}}{PARA 0 "" 0 "" {TEXT -1 0 "" 
}}{SECT 0 {PARA 5 "" 0 "" {TEXT 257 10 "Solution: " }}{PARA 3 "" 0 "" 
{TEXT 264 2 "a)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "int(-2*x^
3 + 6*x, x);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&#\"\"\"\"\"#F&*$
)%\"xG\"\"%F&F&!\"\"*&\"\"$F&)F*F'F&F&" }}}{PARA 3 "" 0 "" {TEXT 265 
1 " " }{TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 278 "Maple does
 not print the constant of integration, ( + C)  but it is understood. \+
  You can add any real number to the above integral to get a different
 integral, i.e. substitute two different values for C.  In this case  \+
\"1\"  and  \"3\" are added to the basic form of the integral." }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 258 1 " " }{TEXT 276 3 "b) " }}
{PARA 0 "" 0 "" {TEXT 263 8 "        " }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 70 "plot(\{-x^4/2 + 3*x^2+1, -x^4/2 + 3*x^2 + 3\}, x = -5
..5, y = -10..10);\n" }}{PARA 13 "" 1 "" {GLPLOT2D 296 162 162 
{PLOTDATA 2 "6&-%'CURVESG6$7hn7$$!\"&\"\"!$!3+++++++lB!#:7$$!3Gmm;HU,
\"*[!#<$!3Vv^8WYlL@F-7$$!3YLLLe%G?y%F1$!3;np^Cmk=>F-7$$!3!***\\(=_+so%
F1$!3jJ^i/eFW<F-7$$!3OmmT&esBf%F1$!3')fN#3()>7e\"F-7$$!3O**\\7`'Gd[%F1
$!38oRy#ft2T\"F-7$$!3ALL$3s%3zVF1$!3s-vbLoP`7F-7$$!3#HLLL)QtrUF1$!3z$y
RwNju5\"F-7$$!3_LL$e/$QkTF1$!3`ux<g<xM(*!#;7$$!35+]7GCadSF1$!3/L/v9V\\
8&)FW7$$!3ommT5=q]RF1$!3C'R@unR\")R(FW7$$!3ILL3_>f_PF1$!3iB5,bnZ!f&FW7
$$!3K++vo1YZNF1$!3_jnMc,6VSFW7$$!3;LL3-OJNLF1$!3MhJ.$>E-v#FW7$$!3p***
\\P*o%Q7$F1$!3@AA&)\\;\"Qt\"FW7$$!3Kmmm\"RFj!HF1$!3@/-_jB[L$*F17$$!33L
L$e4OZr#F1$!3?Bmgn8aZSF17$$!3u*****\\n\\!*\\#F1$\"3'G'eQ9cyTB!#=7$$!3%
)*****\\ixCG#F1$\"3)3[hh(QgeIF17$$!3#******\\KqP2#F1$\"3qC4%R\\>Vl%F17
$$!39LL3-TC%)=F1$\"39dQW>Ka[`F17$$!3[mmm\"4z)e;F1$\"3o[:H$>=#paF17$$!3
Mmmmm`'zY\"F1$\"3D[pYb=#H9&F17$$!3#****\\(=t)eC\"F1$\"3UOy*yb))>X%F17$
$!3!ommmh5$\\5F1$\"3!RA6$4(**pp$F17$$!3S$***\\(=[jL)F_q$\"3-Qc-f`OVGF1
7$$!3)f***\\iXg#G'F_q$\"3oj$4m8Ni5#F17$$!3ndmmT&Q(RTF_q$\"3E![]:ZQ%*\\
\"F17$$!3%\\mmTg=><#F_q$\"3E:0b*H//9\"F17$$!3vDMLLe*e$\\!#?$\"3-`i!*)3
t++\"F17$$\"3!=nm\"zRQb@F_q$\"3Rm4v&G\"HQ6F17$$\"3_,+](=>Y2%F_q$\"3atz
kfMH%[\"F17$$\"3summ\"zXu9'F_q$\"3)fRw&pVKi?F17$$\"3#4+++]y))G)F_q$\"3
D0Z[qG9DGF17$$\"3H++]i_QQ5F1$\"3'GMM'[oU`OF17$$\"3b++D\"y%3T7F1$\"3-n&
Q:XDYV%F17$$\"3+++]P![hY\"F1$\"3ZeJmt9SQ^F17$$\"3iKLL$Qx$o;F1$\"39;)QX
@glZ&F17$$\"3Y+++v.I%)=F1$\"3%*p5T![E%[`F17$$\"3?mm\"zpe*z?F1$\"3?AQg+
%f0i%F17$$\"3;,++D\\'QH#F1$\"3*))\\pd_$4UHF17$$\"3%HL$e9S8&\\#F1$\"3g_
K[K\"*\\uHF_q7$$\"3s++D1#=bq#F1$!3kxPlw-YIQF17$$\"3\"HLL$3s?6HF1$!3G0h
0x+^)[*F17$$\"3a***\\7`Wl7$F1$!3;w(z@V@_u\"FW7$$\"3enmmm*RRL$F1$!3Z(RZ
Gg(yUFFW7$$\"3%zmmTvJga$F1$!3TwG>s/SLSFW7$$\"3]MLe9tOcPF1$!3.-H1'>L>i&
FW7$$\"3yn;H#e0I&QF1$!37x]f&etfY'FW7$$\"31,++]Qk\\RF1$!3=nZjZ]g(Q(FW7$
$\"3%zm;/@-/1%F1$!3$p@MR(yxW&)FW7$$\"3![LL3dg6<%F1$!3gZ%*zJg&f\")*FW7$
$\"3K,+voTAqUF1$!3Xs$Ro&y\\06F-7$$\"3%ymmmw(GpVF1$!3$Q7#Q/#\\&R7F-7$$
\"3/M$eRA5\\Z%F1$!3cr,mPFA%R\"F-7$$\"3C++D\"oK0e%F1$!3!3_y\")3K;c\"F-7
$$\"3m+++]oi\"o%F1$!3N\\q,<OQM<F-7$$\"35,+v=5s#y%F1$!3QG'*))>H'*>>F-7$
$\"3a+]P40O\"*[F1$!3\\-x'HUjV8#F-7$$\"\"&F*F+-%'COLOURG6&%$RGBG$\"#5!
\"\"$F*F*Fh^l-F$6$7hn7$F($!3+++++++XBF-7$F/$!3Vv^8WYl8@F-7$F5$!3;np^Cm
k)*=F-7$F:$!3jJ^i/eFC<F-7$F?$!3')fN#3()>7c\"F-7$FD$!37oRy#ft2R\"F-7$FI
$!3s-vbLoPL7F-7$FN$!3!QyRwNju3\"F-7$FS$!3`ux<g<xM&*FW7$FY$!3/L/v9V\\8$
)FW7$Fhn$!3C'R@unR\")>(FW7$F]o$!3iB5,bnZ!R&FW7$Fbo$!3_jnMc,6VQFW7$Fgo$
!3MhJ.$>E-b#FW7$F\\p$!3@AA&)\\;\"Q`\"FW7$Fap$!3@/-_jB[LtF17$Ffp$!3?Bmg
n8aZ?F17$F[q$\"3H'eQ9cyTB#F17$Faq$\"3)3[hh(Qge]F17$Ffq$\"3qC4%R\\>Vl'F
17$F[r$\"39dQW>Ka[tF17$F`r$\"3o[:H$>=#puF17$Fer$\"3D[pYb=#H9(F17$Fjr$
\"3UOy*yb))>X'F17$F_s$\"3!RA6$4(**pp&F17$Fds$\"3-Qc-f`OV[F17$Fis$\"3oj
$4m8Ni5%F17$F^t$\"3/![]:ZQ%*\\$F17$Fct$\"3E:0b*H//9$F17$Fht$\"3-`i!*)3
t++$F17$F^u$\"3hm4v&G\"HQJF17$Fcu$\"3atzkfMH%[$F17$Fhu$\"3U'Rw&pVKiSF1
7$F]v$\"3D0Z[qG9D[F17$Fbv$\"3'GMM'[oU`cF17$Fgv$\"3-n&Q:XDYV'F17$F\\w$
\"3ZeJmt9SQrF17$Faw$\"39;)QX@glZ(F17$Ffw$\"3%*p5T![E%[tF17$F[x$\"3?AQg
+%f0i'F17$F`x$\"3*))\\pd_$4U\\F17$Fex$\"3ED$[K\"*\\uH#F17$Fjx$!3kxPlw-
YI=F17$F_y$!3G0h0x+^)[(F17$Fdy$!3;w(z@V@_a\"FW7$Fiy$!3Z(RZGg(yUDFW7$F^
z$!3TwG>s/SLQFW7$Fcz$!3.-H1'>L>U&FW7$Fhz$!37x]f&etfE'FW7$F][l$!3=nZjZ]
g(=(FW7$Fb[l$!3$p@MR(yxW$)FW7$Fg[l$!3gZ%*zJg&fh*FW7$F\\\\l$!3Ws$Ro&y\\
&3\"F-7$Fa\\l$!3$Q7#Q/#\\&>7F-7$Ff\\l$!3cr,mPFAu8F-7$F[]l$!3!3_y\")3K;
a\"F-7$F`]l$!3N\\q,<OQ9<F-7$Fe]l$!3QG'*))>H'***=F-7$Fj]l$!3\\-x'HUjV6#
F-7$F_^lF]_l-Fb^l6&Fd^lFh^lFe^lFh^l-%+AXESLABELSG6$Q\"x6\"Q\"yFdjl-%%V
IEWG6$;F(F_^l;$!#5F*$Ff^lF*" 1 2 0 1 10 0 2 9 1 4 2 1.000000 
45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}}{PARA 0 "" 0 "" {TEXT 
-1 1 " " }{TEXT 277 2 "c)" }{TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 200 "Both graphs have the same shape. The graphs have two loc
al maximums, one local minimum and are symmetric to the y-axis.  The s
econd graph is an upward vertical shift of two units of the first grap
h.  " }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 76 
"_____________________________________________________________________
_______" }}{PARA 256 "" 0 "" {TEXT 261 0 "" }{TEXT -1 0 "" }{TEXT 259 
2 "  " }{TEXT 262 10 "ASSIGNMENT" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{SECT 0 {PARA 3 "" 0 "" {TEXT -1 0 "" }{TEXT 266 10 "Problem 1:" }}
{PARA 0 "" 0 "" {TEXT 257 1 " " }{TEXT -1 61 "  a)  Use Maple to find \+
the integral of the function g(x) =  " }{XPPEDIT 18 0 "tan(x)*sec(x)^2
;" "6#*&-%$tanG6#%\"xG\"\"\"*$-%$secG6#F'\"\"#F(" }}{PARA 0 "" 0 "" 
{TEXT -1 52 "                                  NOTE:  Maple uses " }
{XPPEDIT 18 0 "sec(x)^2;" "6#*$-%$secG6#%\"xG\"\"#" }{TEXT -1 18 " to \+
mean (sec x)^2" }}{PARA 0 "" 0 "" {TEXT -1 69 "   b)   Integrate g(x) \+
by hand using the substitution:  Let u = tan x" }}{PARA 0 "" 0 "" 
{TEXT -1 54 "   c)   Use Maple to graph both forms of the integral." }
}{PARA 0 "" 0 "" {TEXT 267 143 "   d)   Explain, using complete senten
ces, how this graph can be used to make an argument for the equivalenc
e of the two forms of the integral." }}{PARA 0 "" 0 "" {TEXT -1 77 "  \+
 e)   Show algebraically that the two forms of the integral are equiva
lent." }}{PARA 0 "" 0 "" {TEXT -1 17 "                 " }{TEXT 260 0 
"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 257 "" 0 "" {TEXT 
-1 10 "Problem 2:" }}{PARA 258 "" 0 "" {TEXT 268 2 "  " }{TEXT 269 
106 "a)   Find another trigonometric function whose indefinite integra
l can be expressed in two different ways." }}{PARA 259 "" 0 "" {TEXT 
270 27 " labels in the explanation." }}{PARA 0 "" 0 "" {TEXT -1 105 " \+
 b)  Use a graph to check to see if your answer is correct.  Explain h
ow the graph supports your result." }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 0 "" }{TEXT 257 20 "Problem 3:  (Rev
iew)" }{TEXT 279 2 "  " }}{PARA 260 "" 0 "" {TEXT -1 203 "Use Maple to
 plot  h(x)  = sin x and its integral on the same graph.  Using at lea
st two specific points as references, write a few sentences explaining
 how the two graphs are related.  Label the graphs." }}}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 81 "_______________________
__________________________________________________________" }}{PARA 0 
"" 0 "" {TEXT -1 101 " MSIP Grant #P120A80089-98: \"Three Urban Calcul
us Reform Programs: Adopting the Best\" 1998-2001      " }}}{MARK "9 8
 2" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }