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Arc length in space works in much the same way as arc length in the plane. For a parameterized space curve s(t) = (x(t),y(t),z(t)), we approximate a small piece of the curve by . Letting as before, we see that ds is really a vector tangent to the curve in space, namely
ds = (x'(t), y'(t), z'(t)) dt
We can then compute the length of the curve by integrating the length |ds| along s(t) to get
Arc
Length from ti to tf
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