' File: XIX_Mass
' Find the  mass for the arc length,  r<t> = <t, 0.2Cosh[t[,0> given the
'   density = D{x,y} =  x^2 + y^2

D{x,y} = x^2 + y^2                    : ' Density for rod path, C: r<t>  above.

X{t} = t                                      :  Xp{t} = Diff[X,t]
Y{t} =  0.2Cosh[t]                     :  Yp{t} = Diff[Y,t]
' - - - - - - - - - - - - - - - - - - - - - - - - - - - -
a = -1   :   b = 1                         ' Given domain for r<t>.
n = 10                                        ' Number of panels = 10 for integration.

F{t} = D{X{t}, Y{t}} * Sqrt[Xp{t}^2 + Yp{t}^2]

ar = Integ[F, {a, b, n, 2}]
' - - - - - - - - - - - - - - - - - - - - - - - - - - - -
' For optional display of r<t> path.
P{t} = 0.2Cosh[t]                      ' Shape of rod to find its mass.
P<t> = <t, P, 0>
Plot[P, {t, -1, 1, n}]

'@Mass = @ar, Units. !



