The py_Evalu spreadsheet was last presented at Scipy Functions with Excel and pyxll 5 – Evaluate with Units and included the Plot_Math function, which converts a text string to Latex format, then uses Matplotlib to convert this to a graphic image, and optionally evaluates the function. To extend this functionality I have now added the Plot_Quad function to evaluate and display definite integrals.

The updated files are included in the py_SciPy zip file that can be downloaded from:

py_SciPy.zip

Details of the required pyxll package (including download, free trial, and full documentation) can be found at: pyxll

For those installing a new copy of pyxll, a 10% discount on the first year’s fees is available using the coupon code “NEWTONEXCELBACH10”.

Examples of the Plot_Quad function are shown on the Latex sheet.

Required inputs are:

• The function to be integrated as a text string.
• The integration limits.
• Any fixed parameters and their values.

When the function is entered the result of the integration is returned in the function cell, and an image of the definite integral is displayed in Latex format immediately below. The image may be selected and dragged to any desired new location, as shown in the second example above. This example returns the area of a circle quadrant, which in this case is accurate to 15 significant figures.

Help on the function can be displayed by clicking on the “insert function” icon, immediately to the left of the edit line, to open the “function wizard”. This shows brief help on each function argument. Detailed help on the SciPy Quad function (used for the evaluation of the integral) can be displayed by clicking on “Help on this function”, at the bottom left of the function wizard display:

By default, the integration variable is “x”. Any other symbol may be specified with the optional “var” argument. Optional arguments for the quad function may also be specified with the “kwargs” argument (see the Scipy help for details of all options). In the example below the epsrel argument has been entered to allow a greater relative error in the result, with in this case only a small reduction in execution time:

In the next example the function has been used to find the force on a circular concrete section generated by a parabolic-rectangular stress distribution, as defined by the Eurocode 2 concrete design code. In this case two separate functions are required, for the rectangular and parabolic part of the stress distribution:

The resulting total force is compared with the results of the py_Circu concrete design function, showing near exact agreement.

The spreadsheet also has an on-sheet check using Simpson’s method with each block divided into 20 layers, showing good (but less exact) agreement: