单词

area of a surface of revolution

释义

area of a surface of revolution

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) (α ≤ θ ≤ β), the surface area equals

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