Prove that the length of a curve as computed using the arc length integral does not depend on its p…

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Prove that the length of a curve as computed using the arc length integral does not depend on its parametrization. More precisely, let 𝒞 be the curve traced by 𝐫(t) for a ≤t ≤b . Let f(s) be a differentiable function such that f^'(s) gt;0 and f(c)=a and f(d)=b . Then 𝐫_1(s)=𝐫(f(s)) parametrizes 𝒞 for c ≤s ≤d . Verify that ∫_a^b𝐫^'(t) d t=∫_c^d𝐫_1^'(s) d s

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