' File: XIX_Line6:  Line integrals of Vector Fields.
' NOTE: For multiple variables, treat each component shown below.
' Find the line integral for the vector field, <x + yz,  y - xz,  z + xy>
'    over C:  (0, 1, 2) --> (3, -1,1)

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

Hx{t} = Fi{R.x, R.y, R.z}         ' Then 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.
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' Ercode = 603 may occur if the problem geneates a negative number to a 
'   fractional power.
a = 0  : b = 1 :  n = 10
a1 = Integ[G, {a, b, n, 2}]

'@Line value = @a1!
'@Exact = 8@!


