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volume of a solid of revolution


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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

Subjects: Mathematics.


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