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I'm trying to calculate the length of a curve from a polynomial in Mathematica and for some reason Integrate doesn't complete, it just runs until I abort the execution.

The polynom:

58.1735 - 36.4175 x + 7.10945 x^2 - 0.538311 x^3 + 0.0138115 x^4

Is a part of an integration like this:

integral

where "koordfitprim" is the polynom above (i.e. what is integrated is in fact the square root of 1 + the above polynom^2).

Any ideas why this wouldn't execute?

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  • $\begingroup$ I assume that the polynomial you quote is the derivative of the polynomial $P(x)$ such that the curve you are trying to find the length of (part of) has equation $y=P(x)$. $\endgroup$ – André Nicolas May 19 '11 at 22:37
  • $\begingroup$ @user6312 yes it is. My first attempt was integrating and deriving all at the same time but as it took forever, I started taking stuff out to see if I could find what was slowing things down. $\endgroup$ – Kalle May 20 '11 at 10:48
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You should try to use NIntegrate (instead of Integrate). Integrate is for symbolic integration. NIntegrate for numerical integration. So try

NIntegrate[Sqrt[1+koordfitprim^2],{x,3,18}]
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  • $\begingroup$ Ohh, I see. Thank you! Wow, that instantly equated. THANK YOU!! $\endgroup$ – Kalle May 19 '11 at 20:45
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This is a very tough integral and you asked Mathematica to evaluate it symbolically i.e. analytically. I am not sure whether it can be calculated at all.

What you wanted was a numerical integral

NIntegrate[Sqrt[1 + ko[x]^2], {x, 3, 18}]

The result is, after a fraction of a second,

59.211531

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    $\begingroup$ What fraction of a second was it... 13/4 ?? $\endgroup$ – The Chaz 2.0 May 19 '11 at 20:53

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