area of a surface of revolution

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Let y=f(x) be the graph of a function f such that f′ is continuous on [a, b] and f(x)≥0 for all x in [a, b]. The area of the surface obtained by rotating, through one revolution about the x-axis, the arc 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 surface area equals

Polar form

For the curve r=r(θ) (αθβ), the surface area equals

Subjects: Mathematics.

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