' File: XIX_Line5:  Line integrals of Vector Fields.
' NOTE: For multiple variables, treat each component shown below.

' Given F{x,y,z} =  (x*z, 0, -y*z)
Fi{x,y,z} = x*z
Fj{x,y,z} = 0
Fk{x,y,z} = -y*z
' - - - - - - - - - - -
'Given the C:  (-1,2,0) --> (3,0,1)  line segment.
X{t} = 4t + 1  :  Y{t} = -2t + 2  :  Z{t} = t    ' Parametric form for line segment.
' - - - - - - - - - - -
R<t> = <X, Y, Z>      : Rp<t> = vDiff[R]

Hx{t} = Fi{R.x, R.y, R.z}         ' Now substitute
Hy{t} = Fj{R.x, R.y, R.z}
Hz{t} = Fk{R.x, R.y, R.z}

H<t> = <Hx, Hy, Hz>             ' And then form vector.
G{t} = sDot[H,Rp]                  ' Form dot product.
' - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
a = 0  : b = 1 :  n = 10
a1 = integ[G, {a, b, n, 2}]

'@Value = @a1!
'@Exact = 7 units@!



