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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "1340ForShowA27.mws\nThu Oc
t 27 13:08:55 MDT 2005\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "
restart:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 34 "Page 98 of our Text -
- Integration" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "Antiderivatives:
  " }{XPPEDIT 18 0 "Int(cos(2*x),x);" "6#-%$IntG6$-%$cosG6#*&\"\"#\"\"
\"%\"xGF+F," }{TEXT -1 11 " via Maple " }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 19 "Int( cos(2*x) , x);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 9 "value(%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "Mapl
e doesn't do \"+ C\"" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 50 "Nobody knows a \+
nice Calculus-I antiderivative for " }{XPPEDIT 18 0 "exp(-x^2);" "6#-%
$expG6#,$*$%\"xG\"\"#!\"\"" }{TEXT -1 1 ":" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "Int(  exp(-x^2), \+
x);   value(%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "Or for " }
{XPPEDIT 18 0 "e^sec(x^2);" "6#)%\"eG-%$secG6#*$%\"xG\"\"#" }{TEXT -1 
1 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "Int(  exp(sec(x^2))
, x);   value(%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "Definite int
egrals " }{XPPEDIT 18 0 "Int(tan(x),x = 0 .. Pi/4);" "6#-%$IntG6$-%$ta
nG6#%\"xG/F);\"\"!*&%#PiG\"\"\"\"\"%!\"\"" }{TEXT -1 1 ":" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "rex := Int( tan(x), x=0..Pi/4);" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "value(rex); evalf(%);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "rex := Int( tan(x), x=0..Pi)
;  value(rex);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "rex := In
t( tan(x), x=0..Pi/2);  value(rex);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 18 "The derivative of " }{XPPEDIT 
18 0 "Int(tan(u),u = 0 .. x);" "6#-%$IntG6$-%$tanG6#%\"uG/F);\"\"!%\"x
G" }{TEXT -1 34 " -- FTC-I in Chapter 5 of 170 text" }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "F := unap
ply(   Int( u^3 - 2*u, u=0..x),  x);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 5 "D(F);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 12 "Section 7.1:" }}{PARA 0 "" 0 "" {TEXT -1 
45 "We now calculate the area under the graph of " }{XPPEDIT 18 0 "f(x
) = e^(-x^2);" "6#/-%\"fG6#%\"xG)%\"eG,$*$F'\"\"#!\"\"" }{TEXT -1 14 "
 from -1 to 2:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 20 "f := x -> exp(-x^2);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 13 "XRG := -1..2:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 28 "Area := Int( f(x) , x=XRG); " }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 20 "evalf( value(Area));" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 68 "Maybe we should plot firs
t to make sure we aren't missing something:" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "plot(f,XRG);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 20 "No
w go for the area:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 12 "value(Area);" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 30 "Broaden the integration range:" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 43 "Int(f(x), x=0..5280);  value(%);  evalf(%);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "Int(f(x), x=0..infinity);  v
alue(%);  evalf(%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "Section 7.
1 in the MATH-171 Text" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 71 "Section 6.1 in the Calculus Text: the area between t
wo curves.  6.1: 36" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 55 "Find the area of the region boxed in by f and g, where \+
" }{XPPEDIT 18 0 "f(x) = 2-x^2;" "6#/-%\"fG6#%\"xG,&\"\"#\"\"\"*$F'F)!
\"\"" }{TEXT -1 5 " and " }{XPPEDIT 18 0 "g(x) = exp(x);" "6#/-%\"gG6#
%\"xG-%$expG6#F'" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 16 "f := x -> 2-x^2;" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 9 "g := exp;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
13 "XRG := -2..1:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "plot([
f,g], XRG, colour=[red, black], legend=[\"f\",\"g\"]);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "A := fsolve(f(x)=g(x), x=-2..-1);" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "B := fsolve(f(x)=g(x), x=
0..1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "Area := Int( f(x)
 - g(x), x=A..B);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "value(%
);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "#####################
#####################" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "43" 0 }
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