Volume and Surface of Solid of Revolution

sarveshgupta
sarveshgupta
@sarveshgupta-txtmu5 • Oct 19, 2024

Ques] The volume of the solid generated by the revolution, about x-axis, of the area bounded by the curve y = f(x), the x-axis and the ordinates x=a, =b is given by
Int a- b pi*y^2 dx

where y = f(x) is continuous, single valued function in the interval a<=x<=b and the curve does not cross the x-axis, the axis of revolution?

Please help with such type of problems how will you solve this type of problem?

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  • skipper
    skipper

    @skipper-wJtaxo • Oct 4, 2009

    This is 1st year calculus. To calculate a solid of revolution first define the "y" curve that will be revolved around the x axis. Start with something simple like a disk or annulus.
    Move up to more complex examples, like say a bell, or a wineglass.

    This gets you into integration by parts.

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