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Is it possible to calculate integrals with Excel? Hi all, I wanted to calculate some functions containing integrals using Excel, but it doesn't seem my Excel can calculate any kind of integral. This video illustrates using the QUADF worksheet function of the ExceLab Add-in to compute several single and multiple integrals in Excel. ExceLab Add-in comprises advanced Excel worksheet.How to do simple numerical integration in Excel using the Gaussian Quadrature method.

Integration in Excel using Gaussian Quadrature Microsoft Excel is a very powerful tool for a surprising range of applications. The built-in library of mathematical functions cover many of the needs in day-to-day design task.However, integrating an arbitrary continuous function in Excel is not one of the built-in function. In many Engineering projects, one often needs to approximate integrals of a continuous function (think calculating power or energy). Fortunately there are ways around this limitation in Excel.The simplest of the methods is the so called 'trapezoidal rule' integration. As the name indicates, we evaluate the function f(x) at a number of points and calaculate the total area (integral) as the sum of the areas of small trapezoids between two points.

So the integral in the interval a,b can be simply estimated by the trapezoid area given by: S = (b-a). f(a) + f(b)/2 Repeat this for many points, hopefully evaluated at very short spaces and you can get a reasonable estimate of the integral. Simple as the method is, it's also the leat accurate of them all. It may be OK for a first-order estimate, but the accuracy can be pretty bad as demonstrated in the example further below. Microsoft Excel Exponential Integral Functions CalculatorThis is especially true when trying to integrate exponential functions which as luck would have it, are extremely common in Engineering problems (and nature in general). Fortunately, there are many alternative methods of integration which are much more precise and are not very computationally intensive either. Most people learn about the Simpson rule for example in an introductory numerical anlysis class.It's an improvement over the trapezoidal method but not that accurate either.

Recently, I learned about a class of methods knows as 'Gaussin Quadrature' that fit the bill perfectly: simple and quite accurate for the effort involved!.Gaussian Quadrature Methods such as the Simpson rule estimate an integral by evaluating a function f(x) at a point equidistant from a and b in each interval a,b. For example, with the Simpson rule, the function needs to be evaluated at x = (a+b)/2 which is exactly the middle of the interval.There is really no reason why it needs to be so. The beauty of Gaussian integration is that is does not fix the evaluation points at a fixed fraction of the interval, but rather it selects them at an optimum point (or points) in the interval. Calculating Integrals In ExcelFigure 1 shows the two-point Gaussian quadrature for example. Note that the number of points can be much larger; the more points the more accurate the estimation.

However, for the purpose of this article we will stick to two-point quadrature. As stated in the first equation, the integral is estimated by evaluating f(x) at two points: x = x1 and x = x2 and multiplying it by two constants c1 and c2. These points are chosen to yield minimum error and the associated formulas are shown below: Figure 1 - The Two-point Gaussian Quadrature Excel Worksheet Example To illustrate this, I made an example spreadsheet available for download.waveticket.

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