' File: XIX_Line4:  Line integrals of Vector Fields.

' Given F{x,y,z} = <8x^2*y*z, 5z, -4x*y>   and   R<t> = <t, t^2, t^3> for curve C.
' NOTE: For multiple variables, treat each component shown below.

Fi{x,y,z} = 8x^2*y*z  
Fj{x,y,z} = 5z
Fk{x,y,z} = -4x*y

R<t> = <t, t^2, t^3>  :  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.
' - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
a = 0  : b = 1 :  n = 10
wk = integ[G, {a, b, n, 2}]

'@Work done = @wk, Units.!
