'  File: XIX_dlb4

' Find the volume given:  z = f(x,y) = 3 - x - 2y 
' x = 3y ; x  = 0 & y = 0  above xy-plane.
' Set z = 0  --> x + 2y = 3
' Substitute y = x/3  above --> x = 9/5 and y = 3/5 at intersection on the  xy-plane.
'Looking down onto the xy-plane, C{x} = x/3 and D{x} = -x/2 + 3/2.

a = 0   :   b = 9/5 
C{x} = x/3   :   D{x} = -x/2 + 3/2
F{x,y} = 3 - x - 2y           ' NOTE: Set F{x,y} = 1 to find the AREA of triangle in xy-plane.
n = 10 : m = n               ' Sample number of panels for trial.
vo = dblint[F, C, D, {a, b, n, m, y}]

' - - - - - - - Optional Plot of 3D polygon. - - - - - - - - See DOC on method.
Sa<t> = <9t/5,  3t/5, 0>
Sb<t> = <9t/5,  -9t/10 +3/2, 0>
Sc<t>= <9t/5, 3t/5, -3t + 3>
Sd<t> = <0, -3t/2 + 3/2, 3t>

Plot[Sa, Sb, Sc, Sd, {t, 0,1,50}]

'@Volulme = @vo, cubic units.!



