Solution to Differential Geometry Problem

 The Problem:

Obtain the arc length s of the curve between x=0, x=2):

f(x) =  x³ / 2   -   x² / 3  

Solution.

f(x) =  x³ / 2   -   x² / 3  

d(f(x) / dx =   3 x² / 2 -  2x/ 3  

(d(f(x) / dx) ² =  (3 x² / 2 -  2x/ 3 ) (3 x² / 2 -  2x/ 3 ) 

=    9 x⁴ / 4  -   2 x³    +   4 x² / 9

Then: 

L  =  ò ² ₀   Ö(1 +  9 x⁴ / 4  -   2 x³    +   4 x² / 9)

=  3.775 units

Check vs. Mathcad computation: