' File: XIX_ArcLen3
' Find the arc length:  y = Sqrt[x]   given the boundary 0 <= x <=4.
' This arc length  cannot be solved because y'(x) used in the  length formula 
'    does not exist at x = 0.  Hence, rewrite the above as x = y^2. 
'    The new limits become:  0 <= y <= 2.
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Y{t} = t                      :  Yp{t} = Diff[Y,t]
X{t} = Y{t}^2             :  Xp{t} = Diff[X,t]

a = 0   : b = 2  :  n = 10

F{t} = Sqrt[Xp{t}^2 + Yp{t}^2]

xx = Integ[F, {a, b, n, 2}]
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ex = ln[Sqrt[17] + 4] / 4 + sqrt[17]                 ' Exact answer for the arc length.

'@ Length = @xx, Units.!
'@ ln[sqrt[17] + 4] / 4 + sqrt[17] = @ex, Units.!


