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Let γ : [c, d] −→ R 3 be a C 1 path and φ :...

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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Answer #1

the orientation preserving mean ist derivative is positive and reversing means its derivative is negative so i have that two cases

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