3 ms·
Closed form integration is fundamentally different. What's the integral of exp( sqrt ( 1 + (tan^(3/2) X)2 ) ) ) ? We only know a handful of forms that can be
by srean 6y ago
Closed form integration is fundamentally different.
What's the integral of exp( sqrt ( 1 + (tan^(3/2) X)2 ) ) ) ?
We only know a handful of forms that can be integrated in closed form and its down to our creativity to discover new forms that can be integrated (same deal with solving differential equations and the reasons are the same).
The forms that we know how to integrate can be done by a computer. CAS tools will do that for you. For example Mathematica.
- adamnemecek 6y agoAre you familiar with automatic differentiation?
- srean 6y agoI am. Try the integration analogue of it on the fairly simple example i gave. The auto-diff of that is a straightforward.
- adamnemecek 6y agoRight. I'm still working out the autoint thing so no. I can't try it right now.
- judofyr 6y agoThe reason why auto-diff is exact and amazing is because (1) the derivative operation is "decomposable" through the chain rule and (2) we've found the symbolic derivative of the basic functions. There's not a mathematical trick in auto-diff which we recently discovered. It's mainly a reformulation of the properties of the derivative which turns out to be useful for computers. Finding an "auto-integrate method" would probably involve finding a way of calculating the integral in a decomposable way, and that indeed would be amazing, but I don't really see that happening any time soon.