单词

volume of a solid of revolution

释义

volume of a solid of revolution

Let y = f(x) be the graph of a function f, a continuous function on [a,b], and such that f(x) ≥ 0 for all x in [a,b]. The volume V of the solid of revolution obtained by rotating, through one revolution about the x-axis, the region bounded by the curve y = f(x), the x-axis and the lines x = a and x = b, is given by

Parametric form

For the curve x = x(t), y = y(t) (t ε [α, β]), the volume V is given by

Compare area of a surface of revolution

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