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  • Subject: [mg26160] RE: [mg26122] Graphics for LOWER INTEGRAL
  • From: "David Park" <djmp at>
  • Date: Thu, 30 Nov 2000 01:04:04 -0500 (EST)
  • Sender: owner-wri-mathgroup at


My DrawingPaperTutorial, which requires the DrawingPaper packages, all
available at my web site, contains an animated Riemann Sum example. It
performs random partitions of the integration interval, and picks x points
randomly within each partition interval. It then draws the rectangles and
the curve. The animation shows how the picture changes and the sum
approaches the integral as the norm of the partition is reduced. However, it
does not show lower and upper bound rectangles, rather it shows the
rectangles that go through the randomly choosen intervalpoints. It would not
be difficult to modify the plot to show the lower and upper bounding

David Park
djmp at

> -----Original Message-----
> From: Ernesto Jardim [mailto:ernesto at]
To: mathgroup at

> Hi
> I'm doing a notebook to demonstrate the Rienman integral and I want to
> include a figure similar to the one there is on the Weistein CRC
> Encyclopedia for LOWER INTEGRAL. I've tried but I wasn't able to do the
> bars under the curve using the lowest f(x) of the curve on the interval
> defined.
> Can you help me ?
> Thanks
> EJ

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