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Suppose we have f(x) = x^{3}.

Integrating this function using the definite integral with the upper boundary being 3 and the lower boundary being 1 would result in 20. Does 20 have any units or is it unitless? Seeing how it is the area underneath a curve, I would imagine that it has square units. If you were to differentiate this function you would get [itex]\frac{dy}{dx}[/itex]=3x^{2}. Does the derivative have any units?

Thanks,

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# Units of a definite integral

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