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Calculate the Integral of …

Choose variable of integration and integration bounds in "Options". Preview of your input:

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Result

Above, enter the function to integrate. Variable of integration, integration bounds and other settings can be changed in "Options". When you're done, click "Go!" to start the integral/antiderivative calculation. The result will be shown below.

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How the Integral Calculator works …

For those with a technical background, the following section explains how the Integral Calculator works.

First, a parser analyzes the mathematical formula. It transforms it into a form that is better understandable by a computer, namely a tree (see figure below). In doing this, the Integral Calculator has to respect the order of operations. A specialty in mathematical formulas is that the multiplication sign can be left out sometimes, for example we write "5x" instead of "5*x". The Integral Calculator has to detect these cases and insert the multiplication sign.

The parser is implemented in JavaScript, based on the Shunting-yard algorithm, and can run directly in the browser. This allows for quick feedback while typing by transforming the tree into a LaTeX formula. MathJax takes care of displaying the formula in the browser.

When the "Go!" button is clicked, the Integral Calculator sends the mathematical formula and the settings (variable of integration and integration bounds) to the server, where it is analyzed again using the same JavaScript code (this is possible using Node.js). This time, the formula gets transformed into a form that can be understood by the computer algebra system Maxima.

How the Integral Calculator works

Maxima takes care of actually computing the integral of the mathematical formula. Maxima's output is transformed to LaTeX again and is then presented to the user. The antiderivative is computed using the Risch algorithm, which is hard to understand for humans. That's why showing the steps of calculation is very challenging for integrals.

The interactive function graphs are computed in the browser and displayed within a canvas element (HTML5). For each function to be graphed, the calculator creates a JavaScript function, which is then evaluated in small steps in order to draw the graph. While graphing, singularities (e. g. poles) are detected and treated specially. The gesture control is implemented using Hammer.js.

If you have any questions or ideas for improvements to the Integral Calculator, don't hesitate to write me an e-mail.

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