arc length

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Let y=f(x) be the graph of a function f such that f′ is continuous on [a, b]. The length of the arc, or arc length, of the curve y=f(x) between x=a and x=b equals

Parametric form

For the curve x=x(t), y=y(t) (t ∈ [α, β]), the arc length equals

Polar form

For the curve r=r(θ) (αθβ), the arc length equals

Subjects: Mathematics.

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