'  File: XIX_dbl2 - - - - - - - Fine the Area of the triangle.
F{x,y} = 1
n = 10  :  m = n  :  '  Panels for accuracy.
' Given triangle coordinates:  (1,1), (0,3), & (4,5)    (A drawing may help.)
' - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
C{x} = -2x+3  :  D{x} = x/2 + 3  :  E{x} = 4x/3 -1/3   ' Equations for the 3 segments.
d1 = dblInt[F, C,D, {0,1,n,m,y}]
' - - - - - - - - - - - - - - - - - - - - - - -
d2 = dblint[F, E,D,{1, 4, n, m,y}]
d = d1 + d2                ' Total area by adding d1 & d2.

' - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
' Optional Plot - - Rewrite line segments equations for Plot command.!
Xa{t}= t            :  Ya{t} = -2t+3     :  Pa<t> = < Xa, Ya, 0>
Xb{t} = 4t         :  Yb{t} = 2t+3      :  Pb<t> = < Xb, Yb, 0>
Xc{t} = 3t + 1   :  Yc{t} = 4t + 1    :  Pc<t> = < Xc, Yc, 0>

Plot[Pa, Pb, Pc, {t, 0, 1, 50}]

'@    D1 = @d1, left area boundary!
'@    D2 = @d2, right area boundary!
'@    D1 + D2 = @d, total area, !
' Review Ch. III file on above optonal three comment fields to plot the output.!


