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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "The square of the wave fun
ction." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "sin(n*Pi*x/L)*sin
(n*Pi*x/L);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$-%$sinG6#**%\"nG\"\"
\"%#PiGF)%\"xGF)%\"LG!\"\"\"\"#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
36 "General case (without limits 0 to L)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 35 "int(sin(n*Pi*x/L)*sin(n*Pi*x/L),x);" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#**,&*&-%$cosG6#**%\"nG\"\"\"%#PiGF+%\"xGF+%\"LG!\"\"
F+-%$sinGF(F+#F/\"\"#F)#F+F3F+F*F/F,F/F.F+" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 25 "The integral from 0 to L." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 40 "int(sin(n*Pi*x/L)*sin(n*Pi*x/L),x=0..L);" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#,$**%\"LG\"\"\",&*&-%$cosG6#*&%\"nGF&%#PiGF&F&-
%$sinGF+F&!\"\"F,F&F&F-F1F.F1#F&\"\"#" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 29 "Now, consider the case n = 1." }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 36 "int(sin(Pi*x/L)*sin(Pi*x/L),x=0..L);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#,$%\"LG#\"\"\"\"\"#" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 11 "Or n = 2..." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 
"int(sin(2*Pi*x/L)*sin(2*Pi*x/L),x=0..L);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,$%\"LG#\"\"\"\"\"#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 11 "Or n = 3..." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "int(s
in(3*Pi*x/L)*sin(3*Pi*x/L),x=0..L);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#,$%\"LG#\"\"\"\"\"#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 49 "Thus, we \+
see that for all n, the integral is L/2." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{MARK "12 0 0" 49 }{VIEWOPTS 1 1 0 1 1 1803 }