http://integrals.wolfram.com/index.jsp
INSIDE THE INTEGRATOR
The Wolfram Mathematica Online Integrator uses webMathematica technology to bring the computational capabilities of Mathematica to the web.
The heart of The Integrator is Mathematica's built-in Integrate function--the same one you use when accessing Mathematica directly. When you type in an integral, the Integrator uses webMathematica to send the integral to the Mathematica kernel, which computes the result using the Integrate function. The result is then embedded into the web page as typeset output.
How the Integrate Function Works
Mathematica's Integrate function represents the fruits of a huge amount of mathematical and computational research. It doesn't do integrals the way people do. Instead, it uses powerful, general algorithms that often involve very sophisticated math. There are a couple of approaches that it most commonly takes. One involves working out the general form for an integral, then differentiating this form and solving equations to match up undetermined symbolic parameters. Even for quite simple integrands, the equations generated in this way can be highly complex and require Mathematica's strong algebraic computation capabilities to solve. Another approach that Mathematica uses in working out integrals is to convert them to generalized hypergeometric functions, then use collections of relations about these highly general mathematical functions.
Mathematica's Integrate function represents the fruits of a huge amount of mathematical and computational research. It doesn't do integrals the way people do. Instead, it uses powerful, general algorithms that often involve very sophisticated math. There are a couple of approaches that it most commonly takes. One involves working out the general form for an integral, then differentiating this form and solving equations to match up undetermined symbolic parameters. Even for quite simple integrands, the equations generated in this way can be highly complex and require Mathematica's strong algebraic computation capabilities to solve. Another approach that Mathematica uses in working out integrals is to convert them to generalized hypergeometric functions, then use collections of relations about these highly general mathematical functions.
How Mathematica Typesetting Works
One of Mathematica's achievements was the introduction of a new generation of capabilities for typesetting mathematical formulas. New algorithms for optimal layout of mathematical formulas, as well as new families of fonts, were developed for Mathematica. In The Integrator, the results of Mathematica's typesetting are automatically converted to GIF. Alternatively, you can request the answer in InputForm, a text-based format, which can be pasted into Mathematica, Word, or other applications.
One of Mathematica's achievements was the introduction of a new generation of capabilities for typesetting mathematical formulas. New algorithms for optimal layout of mathematical formulas, as well as new families of fonts, were developed for Mathematica. In The Integrator, the results of Mathematica's typesetting are automatically converted to GIF. Alternatively, you can request the answer in InputForm, a text-based format, which can be pasted into Mathematica, Word, or other applications.
How webMathematica Works
webMathematica provides the ideal solution to interactive computations over the web. Using J/Link, webMathematica connects Mathematica to your web server, enabling interactive evaluation on your website. For more information about this technology and how it works, see the webMathematica site.
webMathematica provides the ideal solution to interactive computations over the web. Using J/Link, webMathematica connects Mathematica to your web server, enabling interactive evaluation on your website. For more information about this technology and how it works, see the webMathematica site.
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