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Given that a typical cross-section of a solid taken perpendicular to the -axis has an area of , set up an integral to calculate the volume of this solid from . Does it matter what the shape of the solid is? Explain.

Of course every shape has a different area function, and this .
It is not possible to know what the cross-sections looks like. Perhaps they are rectangles with and ? But, they could also be strange looking shapes. As long as all of their , the volume by cross-section formula will work.