       Re: Area under Curve

• To: mathgroup at smc.vnet.net
• Subject: [mg7961] Re: [mg7943] Area under Curve
• From: Andrei Constantinescu <constant at athena.polytechnique.fr>
• Date: Wed, 30 Jul 1997 02:37:25 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```
On Fri, 25 Jul 1997, Sankar Baruah wrote:

> I am new to Mathematica and would really appreciate some pointers from
> experienced users.  I have a 2 variable data set of about 50
> observations.  I want to plot each obseravtion and calculate the area
> under the curve.  How do I do this in Mathematica ?
> Are there examples in the Mathematica Book and/or are there separate
> application notes etc. available ?
> Thanks.
> Sankar.
>
>
>

Hi Sankar,

there is no need to be experienced to solve this problem.
You have many solutions to do this (take also a look at the Mma books):

1. your data is really: {..., {xi, f[xi]}, ... }

- try ListIntegrate
- try an Interpolation + Integration
- write a simple Trapez system as the one below.

2. you data is {..., {xi,yi}, ... } - a closed curve.

- I do not know the function but, the following
simple function functioned pretty well:

Cint[ data_ ] := Module[{mylist,intg},
imax = Length[data];
mylist = Append[ data, data[] ];
intg = 0;
Do[ intg += 0.25 (mylist[[i,2]] + mylist[[i+1,2]])
(mylist[[i+1,1]] - mylist[[i,1]]);
intg += - 0.25 (mylist[[i,1]] + mylist[[i+1,1]])
(mylist[[i+1,2]] - mylist[[i,2]])
, {i,imax} ];
Print[ intg / 4524., "  [MJ /m^3]"]
]

a + andrei

```

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