10 SCREEN 12
20 WINDOW (-1, 5)-(38, -25)
30 LINE (0, 0)-(4, 4)
40 LINE (4, 4)-(4, 0)
90 LINE (-1, 0)-(5, 0)
100 LINE (0, 5)-(0, -1)
110 PAINT (3, 2)
115 LOCATE 1, 20
120 PRINT "Center of Mass by Triple Integral"
130 CIRCLE (3, 9 / 5), .2, 1
140 LOCATE 7, 1
150 PRINT "Problem: Find the center of mass under z^2=xy above y=x,y=0,x=4 in plane z=0"
160 PRINT "       "; CHR$(244); "4"; CHR$(244); "x"; CHR$(244); "(xy)^1/2 "; CHR$(244); "4"; CHR$(244); "x                    "; CHR$(244); "4                   "; CHR$(179); "y=x"
170 PRINT "Mass M="; CHR$(245); "0"; CHR$(245); "0"; CHR$(245); "0 dzdydx="; CHR$(245); "0"; CHR$(245); "0 (x^1/2)(y^1/2)dydx="; CHR$(245); "0 (x^1/2)(2(y^3/2)/3"; CHR$(179); "y=0 dx"
180 PRINT " "; CHR$(244); "4                         "; CHR$(244); "4                        "; CHR$(179); "4"
190 PRINT "="; CHR$(245); "0 (x^1/2)(2/3)x^(3/2)-0dx="; CHR$(245); "0 (2/3)x^2dx=(2/3)(x^3)/3"; CHR$(179); "0 =128/9"
200 PRINT "                 "; CHR$(244); "4"; CHR$(244); "x"; CHR$(244); "(xy)^1/2  "; CHR$(244); "4"; CHR$(244); "x                 "; CHR$(244); "4        "; CHR$(244); "x"
210 PRINT "Moment of yz Myz="; CHR$(245); "0"; CHR$(245); "0"; CHR$(245); "0 xdzdydx="; CHR$(245); "0"; CHR$(245); "0 x(xy)^(1/2)dydx="; CHR$(245); "0 x^(3/2)"; CHR$(245); "0 y^(1/2)dydx"
220 PRINT " "; CHR$(244); "4                            "; CHR$(244); "4                   "; CHR$(179); "4"
230 PRINT "="; CHR$(245); "0 x^(3/2)(2/3)x^(3/2)dx=(2/3)"; CHR$(245); "0 x^3dx=(2/3)(x^4)/4"; CHR$(179); "0 =2(4^3)/3=128/3 <x>=Myz/M"
240 PRINT "        "; CHR$(244); "4"; CHR$(244); "x"; CHR$(244); "(xy)^1/2  "; CHR$(244); "4"; CHR$(244); "x                    "; CHR$(244); "4"
250 PRINT "=3  Mxz="; CHR$(245); "0"; CHR$(245); "0"; CHR$(245); "0 ydzdydx="; CHR$(245); "0"; CHR$(245); "0 y^(3/2)x^(1/2)dydx="; CHR$(245); "0 (2/5)x^(5/2)x^(1/2)dx"
260 PRINT "      "; CHR$(244); "4"
270 PRINT "=(2/5)"; CHR$(245); "0 x^3dx=(2/5)(4^4)/4=128/5 <y>=Mxz/M=9/5"
280 PRINT "    "; CHR$(244); "4"; CHR$(244); "x"; CHR$(244); "(xy)^1/2  "; CHR$(244); "4"; CHR$(244); "x                  "; CHR$(244); "4  "; CHR$(244); "x            "; CHR$(244); "4"
290 PRINT "Mxy="; CHR$(245); "0"; CHR$(245); "0"; CHR$(245); "0 zdzdydx="; CHR$(245); "0"; CHR$(245); "0 (1/2)xydydx=(1/2)"; CHR$(245); "0 x"; CHR$(245); "0 ydydx=(1/2)"; CHR$(245); "0 x(x^2)/2dx"
300 PRINT "      "; CHR$(244); "4"
310 PRINT "=(1/4)"; CHR$(245); "0 x^3dx=(1/4)(4^4)/4=16 <z>=Mxy/M=9/8"
320 PRINT "So the center of mass is at (3,9/5,9/8)"
330 SYSTEM