Monday, December 23, 2024

Solution to Differential Geometry Problem

 The Problem:

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

f(x) =  x/ 2   -   x/ 3  


Solution.

f(x) =  x/ 2   -   x/ 3  

d(f(x) / dx =   3 x/ 2 -  2x/ 3  

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

=    9 x/ 4  -   2 x   +   4 x/ 9

Then: 

L  =  ò 0   Ö(1 +  x/ 4  -   2 x   +   4 x/ 9)


=  3.775 units


Check vs. Mathcad computation:



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