# LaTeX2HTML 96.1 (Feb 5, 1996)
# Associate images original text with physical files.

$key = q/{displaymath}int_0^2piint_0^4(-8rcostheta+12rsintheta-3)rdrdtheta.{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=400 HEIGHT=40 ALIGN=BOTTOM ALT="displaymath69" SRC="img7.gif"  > '; 
$key = q/{displaymath}int_CbfFcdotdbfr=intint_S(rmcurlbfFcdotbfn)dS{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=361 HEIGHT=36 ALIGN=BOTTOM ALT="displaymath57" SRC="img1.gif"  > '; 
$key = q/{displaymath}int_CbfFcdotdbfr=int_0^2pibfF(x(t),y(t),z(t))cdotr'(t)dt{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=404 HEIGHT=40 ALIGN=BOTTOM ALT="displaymath59" SRC="img2.gif"  > '; 
$key = q/{displaymath}int_0^4(-8r^2costheta+12r^2sintheta-3r)dr=-4r^2costheta+6r^2sintheta-3r^22|_r=0^r=4{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=531 HEIGHT=40 ALIGN=BOTTOM ALT="displaymath71" SRC="img8.gif"  > '; 
$key = q/{displaymath}int_0^2pi(-64costheta+144sintheta-24)dtheta=-64sintheta-144costheta-24theta|^2pi_0=-48pi{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=560 HEIGHT=40 ALIGN=BOTTOM ALT="displaymath75" SRC="img10.gif"  > '; 
$key = q/{displaymath}intint_SrmcurlbfFcdotndS=intint_R;SPMlt;-4,6,-3;SPMgt;cdot;SPMlt;2x,2y,1;SPMgt;dA{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=470 HEIGHT=36 ALIGN=BOTTOM ALT="displaymath65" SRC="img5.gif"  > '; 
$key = q/{displaymath}-64costheta+144sintheta-24{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=345 HEIGHT=15 ALIGN=BOTTOM ALT="displaymath73" SRC="img9.gif"  > '; 
$key = q/{displaymath}rmcurlbfF=;SPMlt;R_y-Q_z,P_z-R_x,Q_x-P_y;SPMgt;.{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=407 HEIGHT=18 ALIGN=BOTTOM ALT="displaymath63" SRC="img4.gif"  > '; 
$key = q/{displaymath}intint_R(-8x+12y-3)dA,{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=343 HEIGHT=36 ALIGN=BOTTOM ALT="displaymath67" SRC="img6.gif"  > '; 
$key = q/{displaymath}int_0^2pi-48sin^2tdt=-48pi.{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=345 HEIGHT=40 ALIGN=BOTTOM ALT="displaymath61" SRC="img3.gif"  > '; 

1;

