Integrating a set of data points

[Mu naught]

Homework Statement

I have a set of data points, and I need to find the area under the curve they form. I am trying to use Maple for this, by using the PolynomialInterpolation() to fit a curve to my list of points. I then would just integrate this function over the appropriate interval.

The problem is it that although the function it spits out gives me accurate range when I type in values manually, when I try to integrate it over the correct interval it spits out a huge number which is vastly larger than the area under the curve could be.

So now I don't know how to do this... is there another way to get the area?

The Attempt at a Solution

 

[LCKurtz]

An interpolating polynomial will be exact at the interpolating points but may fluctuate wildly between them consequently not being at all appropriate. If the points are equally spaced on the x-axis you might try the trapezoidal formula or Simpson's rule. Alternatively you could let Maple use a spline interpolation and work out the integral both.