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ganesh
Posts:
37
Registered:
2/15/06


Evaluating integral for length of the curve.
Posted:
Sep 27, 2012 6:48 AM


I have a curve defined by following parametric equation:
?(?)=1+0.5×cos(N?)(cos(?),sin(?)),0???2?
I need to calculate the length of the curve between say ? = 0 to ? = 1.0. Formula for calculating the arc length of a curve in polar form is well known (see http://mathworld.wolfram.com/ArcLength.html Eq. 17 therein).
For N = 10, r is given as
r=1+0.5×cos(10?)
and
drd?=?0.5×sin(10?)
The problem is I can't evaluate the integral in Eq. 17 from the Mathworks link for the above equation explicitly. Obviously one can use Matlab ( with trapz command ) to evaluate the integral for given limits but I want an explicit expression for the indefinite integral in terms of generic ?1 and ?2 ( I have hundreds of such integrals to evaluate and difference between ?1 and ?2 is not constant) How do I evaluate the integral? Is there a substitution possible?
Many thanks for help.



