{VERSION 3 0 "IBM INTEL NT" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 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 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "Int(sin(x),x) = int( sin(x),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\$IntG6\$-%\$sinG6#%\"xG F*,\$-%\$cosGF)!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "Int(s in(x),x=0..Pi) = int(sin(x),x=0..Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\$IntG6\$-%\$sinG6#%\"xG/F*;\"\"!%#PiG\"\"#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 88 "A triple integral in spherical polar coordinates ove r the volume of a sphere of radius a" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 40 "First define a function to be integrated" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 26 "f:=exp(-r/a)*cos(theta)^2;" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"fG*&-%\$expG6#,\$*&%\"rG\"\"\"%\"aG!\"\"!\"\"\"\"\" )-%\$cosG6#%&thetaG\"\"#F," }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 239 "Int egrate the radial coordinate from 0 to a, and assign the result to the varable g.. Note that dv = r^2 sin(theta) dr d(theta) d(phi). This fi rst line introduces the r^2 sin(theta) factor, which then carries thro ugh to the other integrals" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "g:=int(f*r^2*sin(theta),r=0..a);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%\"gG,&**-%\$expG6#!\"\"\"\"\")-%\$cosG6#%&thetaG\"\"#\"\"\"-%\$sinGF/ F+)%\"aG\"\"\$F2!\"&*(F,F2F3F2F5F2F1" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 83 "Integrate the polar coordinate from 0 to Pi, and assign the res ult to the varable h" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "h:= int(g,theta=0..Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"hG,&*&-%\$ex pG6#!\"\"\"\"\")%\"aG\"\"\$\"\"\"#!#5F.*\$F,F/#\"\"%F." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 74 "Intergrate the azimuthal coordinate from 0 to 2 Pi to get the final result," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "int(h,phi=0..2*Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*(-%\$expG 6#!\"\"\"\"\")%\"aG\"\"\$\"\"\"%#PiGF)#!#?F,*&F*F-F.F-#\"\")F," }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "9 0 0" 73 } {VIEWOPTS 1 1 0 1 1 1803 }