[c, d] R 3 be a C 1 path and : [a, b] [c, d] be a C 1 one-to one and onto map. Show that and have the same arclength.
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Let γ : [c, d] −→ R 3 be a C 1 path and φ : [a, b] −→ [c, d] be a C 1 one-to one and onto map. Show that

γ and γ ◦ φ have the same arclength. [Note that there are two cases depending on whether φ is orientation preserving or reversing.]

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