Every time you use u-sub, you're actually transforming your region into a different one with equal areapic.twitter.com/hFyRPqd9wb
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Just substitute u=x^2, in fact all possible subtitutions like u=e^x etc. transform an integral in such a way that the area is preserved i.e. an invariant. This can also be shown for multi dimensional/multiple integrals wherea Jacobian /Jacobi ("J") determinant is used.
this is precisely what it did.. the purpose of this video is giving an intuition for what that substitution is actually doing..
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Great, in Europe (e.g. NL) the terminology like u-sub(stitution) is not (quite) common, that was the reason I elaborated a little more on this. We use substitution of variables in general it can also be a t, p, w, z or v etc. I could not resist to elaborate a little on 4-Vol;-)Thanks. Twitter will use this to make your timeline better. UndoUndo
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