Microsoft Excel Exponential Integral Function Approximation

MICROSOFT EXCEL EXPONENTIAL INTEGRAL FUNCTION APPROXIMATION CODE CHECKS IF

Electronic resolution is approximated by pulser line width (FWHM) or RMS.The trapezoidal rule works by approximating the region under the function f(x) graph as a trapezoid and calculating its area. Forecast function in Excel post on the Microsoft.According to Wikipedia: вЂњThe trapezoidal rule is a technique for approximating the definite integral:28 25 jH( )j2 for step function with N 30, d 0:001 m, and 0:004 m. Use a technique called Least Squares Approximation. Excel Functions for Exponential.

The method involves the SUMPRODUCT function, the syntax of which is given below:SUMPRODUCT(array1, , , вЂ¦)The SUMPRODUCT function multiplies the corresponding components in the given arrays and returns the sum of these products. However, the difficulty level is a little bit higher than the first method (especially if you are new to Excel). The picture above contains the entire set of calculations.With this method, you avoid the intermediate calculations, and by using only one function, you get the result. For the first point the result was (1 вЂ“ 0)*(4 + 0)/2 = 2, for the second (2 вЂ“ 1)*(16 + 4)/2 = 10 and so on. For example, in the sample workbook, we had the function y = 4*x^2 we knew 10 points, so we applied the formula 9 times.

Microsoft Excel Exponential Integral Function Approximation Code Checks If

So, you only have to insert the input ranges in the function, and the function will return the curve area. If something goes wrong, the function returns an error message instead of the value. The code checks if the x and y values are (valid) ranges and if the x and y ranges are equal (for example, if the input is 10 x values and 10 y values).

How do we know that 972 is the right one? The answer is simple: for the particular example, the curve was based on the function y = 4* x^2. If in the specific example we knew 20 points (step 0.5) instead of 10 (step 1), then the result with 3 methods would be 973.5.If we knew 901 points (step 0.01), the result would be around 972, which is the correct one. The more points you know, the more the trapezoids, so the better the approximation (for a specific range). Unfortunately, this is not true!The accuracy of the trapezoidal rule is firmly related to the number of known curve points. You might believe that since the 3 methods agree on the final value, this is the correct one. In the sample workbook, you will notice that, for the particular curve, all 3 different ways that were described above result in the same value (978).

Please enable macros before using it. If it is, you should use the abs function (returns the absolute value of a number) in the first two methods to get the correct area, while the custom VBA function has already implemented it.The file can be opened with Excel 2007 or newer. They are not the same since the area cannot be negative by definition!When you use the trapezoidal rule to calculate a curve area, you have to be careful in cases where the curve is below the x or y-axis. Furthermore, be careful not to confuse the curve area with the value of the definite integral. The more points you have, the better the results you get.