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mathman

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Since the function f(x) is not parallel to the x axis the area differential has to take into account that effect, which for your problem is √2.

In general, you need the differential of arc length of the revolving figure which is

√(1+y'²)dx.

In general, you need the differential of arc length of the revolving figure which is

√(1+y'²)dx.

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mathman

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HallsofIvy

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The

But if we, instead, use the length of the broken line to approximate the length of the line, each segment has length 1/n and there are 2n such segments so that we get a length of

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