An extremely well-written book for students taking Calculus for the first time as well as those who need a refresher. This book makes you realize that Calculus isn't that tough after all. → to the book
The Integral Calculator lets you calculate integrals of functions online!
The calculator supports definite and indefinite integrals (antiderivatives) as well as integrating functions with many variables.
With the Integral Calculator you can check your solutions to calculus exercises. It doesn't show a step by step integration and is not meant to be used for cheating!
For more about how to use the Integral Calculator, go to "Help" or take a look at the examples.
Set integration variable and bounds in "Options". Check your input:
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Not what you mean?
Use parentheses, if necessary, or refer to the help.
Enter a formula into the Integral Calculator above. Click "Go!" to calculate the integral and display it.
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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 (integration variable 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.
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.
If you have any questions or ideas for improvements to the Integral Calculator, don't hesitate to write me an e-mail.
© David Scherfgen 2012 — all rights reserved.
