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{SECT 0 {PARA 0 "" 0 "" {TEXT -1 96 "Name ___________________________ \+
                       BC Calculus                        SHW 2" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 256 45 "Formulas
 for Arc (Curve) Length in the Plane:" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#/*&%8Arc~Length~for~a~curve~G\"\"\"%\"yGF&*(-%\"fG6#%\"xGF&%%:~~~GF
&-%$IntG6$*$,&F&F&*$)-%$f~'GF+\"\"#F&F&#F&F7/F,;%\"aG%\"bGF&" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#/*&%8Arc~Length~for~a~curve~G\"\"\"%\"xGF&*(
-%\"gG6#%\"yGF&%%:~~~GF&-%$IntG6$*$,&F&F&*$)-%$g~'GF+\"\"#F&F&#F&F7/F,
;%\"cG%\"dGF&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&%CArc~Length~for~a
~parametric~curve~G\"\"\"7$%\"xG%\"yGF&*(7$-F(6#%\"tG-F)F-F&%%:~~~GF&-
%$IntG6$*$,&*$)-%$x~'GF-\"\"#F&F&*$)-%$~y'GF-F:F&F&#F&F:/F.;&F.6#F&&F.
6#F:F&" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 259 
160 "Arc Length Exercises.  Note that, in order to do some of the arc \+
length exercises, you may need to solve one or more of the indefinite \+
integral exercises first." }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 257 "" 1 "" {XPPMATH 20 "6$/*&%<Arc~Length~Exercise~2.1:~
~~G\"\"\"%\"yGF&,$*(\"\"#F&\"\"$!\"\",&*$)%\"xGF*F&F&F&F,#F+F*F&/F0;F&
F+" }}{PARA 258 "" 1 "" {XPPMATH 20 "6$/*&%<Arc~Length~Exercise~2.2:~~
~G\"\"\"%\"yGF&,$*&\"\"$!\"\",&*$)%\"xG\"\"#F&F&F0F&#F*F0F&/F/;\"\"!F&
" }}{PARA 259 "" 1 "" {XPPMATH 20 "6$/*&%<Arc~Length~Exercise~2.3:~~~G
\"\"\"%\"yGF&-%#lnG6#-%$secG6#%\"xG/F.;\"\"!,$*&\"\"%!\"\"%#PiGF&F&" }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PAGEBK }{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT 257 21 "Integration by Parts:" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#/-%\"dG6#*&%\"uG\"\"\"%\"vGF),&*&%#duGF)F*F)F)*&
%#dvGF)F(F)F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$%!G%%(uv)G,
&-F%6$%\"vG%\"uG\"\"\"-F%6$F-F,F." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/
-%$IntG6$%\"uG%\"vG,&*&F'\"\"\"F(F+F+-F%6$F(F'!\"\"" }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 258 47 "Indefinite Integral (A
ntiderivative) Exercises." }}{PARA 260 "" 1 "" {XPPMATH 20 "6#*&%FInde
finite~Integrals~Exercise~2.1:~~~G\"\"\"-%$IntG6$*&%\"xGF%-%$sinG6#F*F
%F*F%" }}{PARA 261 "" 1 "" {XPPMATH 20 "6#*&%FIndefinite~Integrals~Exe
rcise~2.2:~~~G\"\"\"-%$IntG6$-%#lnG6#%\"xGF,F%" }}{PARA 262 "" 1 "" 
{XPPMATH 20 "6#*&%FIndefinite~Integrals~Exercise~2.3:~~~G\"\"\"-%$IntG
6$*&%\"xGF%-%$expG6#F*F%F*F%" }}{PARA 263 "" 1 "" {XPPMATH 20 "6#*&%FI
ndefinite~Integrals~Exercise~2.4:~~~G\"\"\"-%$IntG6$*&)%\"xG\"\"#F%-%$
expG6#F+F%F+F%" }}{PARA 264 "" 1 "" {XPPMATH 20 "6#*&%FIndefinite~Inte
grals~Exercise~2.5:~~~G\"\"\"-%$IntG6$*&)%\"xG\"\"$F%-%$expG6#F+F%F+F%
" }}{PAGEBK }{PARA 11 "" 0 "" {TEXT -1 0 "" }}{PARA 265 "" 1 "" 
{XPPMATH 20 "6#*&%FIndefinite~Integrals~Exercise~2.6:~~~G\"\"\"-%$IntG
6$*&-%$expG6#%\"xGF%-%$sinGF,F%F-F%" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{PARA 266 "" 1 "" {XPPMATH 20 "6#*&%FIndefinite~Integrals~Exercise~2.
7:~~~G\"\"\"-%$IntG6$-%$secG6#%\"xGF,F%" }}{PARA 267 "" 1 "" {XPPMATH 
20 "6#*&%FIndefinite~Integrals~Exercise~2.8:~~~G\"\"\"-%$IntG6$*$)-%$s
ecG6#%\"xG\"\"#F%F.F%" }}{PARA 268 "" 1 "" {XPPMATH 20 "6#*&%FIndefini
te~Integrals~Exercise~2.9:~~~G\"\"\"-%$IntG6$*$)-%$secG6#%\"xG\"\"$F%F
.F%" }}{PARA 269 "" 1 "" {XPPMATH 20 "6#*&%GIndefinite~Integrals~Exerc
ise~2.10:~~~G\"\"\"-%$IntG6$*&)%\"xG\"\"#F%-%$expG6#*&%\"aGF%F+F%F%F+F
%" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 
39 "SHW2: Arc Length & Indefinite Integrals" }}{EXCHG {PARA 256 "" 0 "
" {TEXT -1 10 "Arc Length" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 265 "`Arc \+
Length for a curve `*y = f(x)*`:   `*Int(sqrt(1+(`f '`(x))^2),x=a..b);
\n`Arc Length for a curve `*x = g(y)*`:   `*Int(sqrt(1+(`g '`(y))^2),y
=c..d);\n`Arc Length for a parametric curve `*[x,y]=[x(t),y(t)]*`:   `
*\nInt(sqrt((`x '`(t))^2+(` y'`(t))^2),t=t[1]..t[2]);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#/*&%8Arc~Length~for~a~curve~G\"\"\"%\"yGF&*(-%\"fG
6#%\"xGF&%%:~~~GF&-%$IntG6$*$,&F&F&*$)-%$f~'GF+\"\"#F&F&#F&F7/F,;%\"aG
%\"bGF&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&%8Arc~Length~for~a~curve
~G\"\"\"%\"xGF&*(-%\"gG6#%\"yGF&%%:~~~GF&-%$IntG6$*$,&F&F&*$)-%$g~'GF+
\"\"#F&F&#F&F7/F,;%\"cG%\"dGF&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&%
CArc~Length~for~a~parametric~curve~G\"\"\"7$%\"xG%\"yGF&*(7$-F(6#%\"tG
-F)F-F&%%:~~~GF&-%$IntG6$*$,&*$)-%$x~'GF-\"\"#F&F&*$)-%$~y'GF-F:F&F&#F
&F:/F.;&F.6#F&&F.6#F:F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 23 "Arc Length Exercises 1." }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "n:=2:\n`Arc Length Exercise `||n||`
.1:   `*y=(2/3)*(x^2-1)^(3/2),x=1..3;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 65 "`Arc Length Exercise `||n||`.2:   `*y=(1/3)*(x^2+2)^(3/2),x=0..1
;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "`Arc Length Exercise `||n||`.3
:   `*y=ln(sec(x)),x=0..Pi/4;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6$/*&%<Arc~Length~Exercise~2.1:~~~G\"\"
\"%\"yGF&,$*(\"\"#F&\"\"$!\"\",&*$)%\"xGF*F&F&F&F,#F+F*F&/F0;F&F+" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6$/*&%<Arc~Length~Exercise~2.2:~~~G\"\"
\"%\"yGF&,$*&\"\"$!\"\",&*$)%\"xG\"\"#F&F&F0F&#F*F0F&/F/;\"\"!F&" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6$/*&%<Arc~Length~Exercise~2.3:~~~G\"\"
\"%\"yGF&-%#lnG6#-%$secG6#%\"xG/F.;\"\"!,$*&\"\"%!\"\"%#PiGF&F&" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 256 "" 0 "
" {TEXT -1 20 "Integration by Parts" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
76 "'d'(u*v)=du*v+dv*u;\nInt(``,`(uv)`)=Int(v,u)+Int(u,v);\nInt(u,v)=u
*v-Int(v,u);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"dG6#*&%\"uG\"\"\"
%\"vGF),&*&%#duGF)F*F)F)*&%#dvGF)F(F)F)" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#/-%$IntG6$%!G%%(uv)G,&-F%6$%\"vG%\"uG\"\"\"-F%6$F-F,F." }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$%\"uG%\"vG,&*&F'\"\"\"F(F+F+-F%6$F
(F'!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 256 "" 0 "" {TEXT -1 23 "Indefinite Integrals 1." }}{PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 638 "`Indefinite Integrals Exercise `||n||`.1:   `
*Int(x*sin(x),x);\n`Indefinite Integrals Exercise `||n||`.2:   `*Int(l
n(x),x);\n`Indefinite Integrals Exercise `||n||`.3:   `*Int(x*exp(x),x
);\n`Indefinite Integrals Exercise `||n||`.4:   `*Int(x^2*exp(x),x);\n
`Indefinite Integrals Exercise `||n||`.5:   `*Int(x^3*exp(x),x);\n`Ind
efinite Integrals Exercise `||n||`.6:   `*Int(exp(x)*sin(x),x);\n`Inde
finite Integrals Exercise `||n||`.7:   `*Int(sec(x),x);\n`Indefinite I
ntegrals Exercise `||n||`.8:   `*Int(sec(x)^2,x);\n`Indefinite Integra
ls Exercise `||n||`.9:   `*Int(sec(x)^3,x);\n`Indefinite Integrals Exe
rcise `||n||`.10:   `*Int(x^n*exp(a*x),x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#*&%FIndefinite~Integrals~Exercise~2.1:~~~G\"\"\"-%$IntG
6$*&%\"xGF%-%$sinG6#F*F%F*F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%FIn
definite~Integrals~Exercise~2.2:~~~G\"\"\"-%$IntG6$-%#lnG6#%\"xGF,F%" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%FIndefinite~Integrals~Exercise~2.
3:~~~G\"\"\"-%$IntG6$*&%\"xGF%-%$expG6#F*F%F*F%" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#*&%FIndefinite~Integrals~Exercise~2.4:~~~G\"\"\"-%$IntG
6$*&)%\"xG\"\"#F%-%$expG6#F+F%F+F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
*&%FIndefinite~Integrals~Exercise~2.5:~~~G\"\"\"-%$IntG6$*&)%\"xG\"\"$
F%-%$expG6#F+F%F+F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%FIndefinite~
Integrals~Exercise~2.6:~~~G\"\"\"-%$IntG6$*&-%$expG6#%\"xGF%-%$sinGF,F
%F-F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%FIndefinite~Integrals~Exer
cise~2.7:~~~G\"\"\"-%$IntG6$-%$secG6#%\"xGF,F%" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#*&%FIndefinite~Integrals~Exercise~2.8:~~~G\"\"\"-%$IntG
6$*$)-%$secG6#%\"xG\"\"#F%F.F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%F
Indefinite~Integrals~Exercise~2.9:~~~G\"\"\"-%$IntG6$*$)-%$secG6#%\"xG
\"\"$F%F.F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%GIndefinite~Integral
s~Exercise~2.10:~~~G\"\"\"-%$IntG6$*&)%\"xG\"\"#F%-%$expG6#*&%\"aGF%F+
F%F%F+F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{MARK "35
 0 0" 39 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 
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