       Re: Graphics for LOWER INTEGRAL

• To: mathgroup at smc.vnet.net
• Subject: [mg26151] Re: Graphics for LOWER INTEGRAL
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Thu, 30 Nov 2000 01:03:58 -0500 (EST)
• Organization: Universitaet Leipzig
• References: <8vvpf7\$30p@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

since MathWorld is off line I have no idea how the picture may look like
but

LowerSumGraph[f_, {x_, x1_, x2_, n_Integer}, opts___] :=
Module[{data},
data = Table[{x, f}, {x, x1, x2, (x2 - x1)/(n - 1)}];
Show[Plot[f, {x, x1, x2}, DisplayFunction -> Identity, opts],
Graphics[Rectangle @@@ Drop[Transpose[{data, RotateLeft[data]}],
-1] /.
Rectangle[{t1_, y1_}, {t2_, y2_}] :>
Rectangle[{t1, 0}, {t2, If[y2 < y1, y2, y1]}] /.

Rectangle[{t1_, 0}, {t2_, y1_}] :> {GrayLevel[0.5],
Rectangle[{t1, 0}, {t2, y1}], {GrayLevel,
Line[{{t1, 0}, {t2, 0}, {t2, y1}, {t1, y1}, {t1, 0}}]}}
], DisplayFunction -> \$DisplayFunction
]
]

and

LowerSumGraph[x^2, {x, -1, 1, 16}]

Will reproduce the common picture.

Hope that helps
Jens

Ernesto Jardim wrote:
>
> 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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