Home | 18.01 | Chapter 12 | Section 12.2

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When we divide the interval of integration into pieces, we here choose the pieces to all have the same size. This is not necessary; we could allow the pieces to vary in size as long as the longest piece approaches zero eventually, and demand that the resulting sum approach the same thing for any sequence of   pieces such that all sizes approach zero. If we do this, a Riemann sum is still a Riemann sum after we change our variable of integration by substitution.