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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "#The region files ar
e graphs of regions used in triple integration" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 64 "#This one is for the region of intersection of
 the two cylinders" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "# x^2
+y^2=1 and x^2+z^2=1 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "#T
he general form for x: a<=x<=b (a is left, b is right)" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "# for y: f(x)<=y<=g(x) (f(x) is fro
nt, g(x) is rear) " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "# for
 z: F(x,y)<=z<=G(x,y) (F(x,y) is bottom, G(x,y) is top)" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "front:=x->-sqrt(1-x^2);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "rear:=x->sqrt(1-x^2);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "left:=-1; right:=1;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "n:=21;m:=9;" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 24 "top:=(x,y)->sqrt(1-x^2);" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 28 "bottom:=(x,y)->-sqrt(1-x^2);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "xstep:=i->left+i*(right-left)/n;" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "ystep:=(i,j)->front(xstep(
i))+j*(rear(xstep(i))-front(xstep(i)))/m;" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 96 "Top:=[seq([seq([xstep(i), evalf(ystep(i,j)), evalf(
top(xstep(i),ystep(i,j)))],j=0..m)],i=0..n)]:" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 102 "Bottom:=[seq([seq([xstep(i), evalf(ystep(i,j)),
 evalf(bottom(xstep(i),ystep(i,j)))],j=0..m)],i=0..n)]:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 152 "Front:=[seq([[xstep(i), evalf(yste
p(i,0)), evalf(bottom(xstep(i),ystep(i,0)))],[xstep(i), evalf(ystep(i,
0)), evalf(top(xstep(i),ystep(i,0)))]],i=0..n)]:" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 151 "Rear:=[seq([[xstep(i), evalf(ystep(i,m)), ev
alf(bottom(xstep(i),ystep(i,m)))],[xstep(i), evalf(ystep(i,m)), evalf(
top(xstep(i),ystep(i,m)))]],i=0..n)]:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 165 "Left:=[[seq([xstep(0), evalf(ystep(0,j)), evalf(bott
om(xstep(0),ystep(0,j)))],j=0..m)],[seq([xstep(0), evalf(ystep(0,j)), \+
evalf(top(xstep(0),ystep(0,j)))],j=0..m)]]:" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 166 "Right:=[[seq([xstep(n), evalf(ystep(n,j)), evalf(
bottom(xstep(n),ystep(n,j)))],j=0..m)],[seq([xstep(n), evalf(ystep(n,j
)), evalf(top(xstep(n),ystep(n,j)))],j=0..m)]]:" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 80 "a:=PLOT3D(MESH(Top),MESH(Bottom),MESH(Front),M
ESH(Rear),MESH(Left),MESH(Right)):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 92 "with(plots):display(a,scaling=constrained,axes=BOXED,
title=`intersection of two cylinders`);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{MARK "23" 0 }{VIEWOPTS 1 1 0 3 2 1804 1 1 1 1 }
{PAGENUMBERS 0 1 2 33 1 1 }