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Topic: Evaluating integral for length of the curve.
Replies: 1   Last Post: Sep 27, 2012 12:24 PM

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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
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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.



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