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I want to get the arclength of a parametric function. For t -5..5.How can I get this ? And how can I set the nticks right here in the function to get more precise results? Something with Phytagoras?

 f(t):= t^2 -4*t:
 g(t):= t12 -2*t +3;
AngularLover
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  • Arc length is a property of a curve, not a function. (For example, if F is a function that assigns to each student his or her favourite subject, there is no natural concept of 'arc length'.) – Andreas Rejbrand Dec 13 '14 at 15:48

1 Answers1

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It is known that arc length of parametric curve is

L=Integral[t=a..b](ds)

where 

ds = Sqrt(f'(t)^2 +g'(t)^2)dt

here

ds = Sqrt((2t-4)^2+(2t-2)^2)dt = 
     Sqrt(4t^2-16t+16+4t^2-8t+4)dt=
     2*Sqrt(2t^2-6t+5)dt

To get integral, you can use wolframalpha service.
It is possible to calculate value of this integral in limits (79.5), but I suspect that general formula is more useful.

MBo
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