![]() Since the integral is only nonzero on that axis, take its real part to obtain the value of the desired integral. The Wolfram Language has integrated interactive and programmatic access to the full power of the WolframAlpha computational knowledge engine, using it to allow free-form linguistic input of computations and programs, as well as extensive data and computation capabilities that rely on the WolframAlpha knowledgebase. ![]() Hence, the complex contour integral derives its value entirely from the integral over the real axis. We can show that, since e^(iz) is bounded in magnitude by 1, that the contour integral over the circular part goes to 0 as R –> inf. * Consider the limit of this integral as R –> infinity. The integral over the real segment is the same as the real integral in the context you’re used to. * Notice that this integral can be decomposed into two parts: an integral over a semicircular arc with nonzero imaginary part traced from (R, 0) to (-R, 0) parameterized by (R cos t, R sin t) on (0, pi), and an integral over a real line segment from -R to R. * Use your complex variables theorem of choice (a calculation of residues, together with the Cauchy residue theorem, will make short work of the contour integral of f around the semicircle C_R). describes this process in more detail than I care to, but in a nutshell, the idea goes like this: * Treat the integrand as a function of a complex variable, and note that, on the real axis, cos z/ = Re e^(iz)/ = Re f(z) * Consider the contour integral of f(z) around a semicircle, centered at the origin and oriented counter-clockwise, of radius R (if you’ve studied any multivariable calculus, this is analogous to a path or line integral in two real dimensions). This is covered as a standard application in a first course on complex analysis, but it really is quite fascinating. MathPhD is right (as, with a handle such as that, we would hope): the exact computation of this integral is a very neat application of complex variables to real-valued functions. ![]() I hope this is what you mean by “line integral”)įor the best answers, search on this site Maybe we can find a way to get it to do some of your problems and you can see the result of the ad hoc methods I have used to coax WolframAlpha into cooperating and if that works then maybe you can guess how you might try similar things and see if it can solve some of your problems you are really interested in.Is it possible to calculate a line integral in wolfram alpha, and if so what would be the form I would have to put it in? to approach it to do a triple integral, and you could approach it any way you want. ![]() Then you might include a couple of intermediate sized problems and finally an example or two of the kind/size problems that you really want to do. Yeah, someone had to write Wolfram Alpha, you know, some of you. If you can show one or a few of the simplest shortest Selberg Integrals that you are interested in then I will take a moment and see if I can find a way to coax WolframAlpha into doing those for you. And for the rest of all the problems that might be posed my response is usually "I don't know of a way to format that so that WolframAlpha will understand and I suggest that you get a 'grad student 2.0' to solve that for you." Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. Sometimes the line length limit can be avoided by breaking the problem down into a sequence of simpler problems, giving each one to WolframAlpha and finally reassembling the individual results into a complete solution. For some problems that process is fairly straight forward, sometimes it requires a few tricks. I am guessing that limit may be one of the issues that you may face in trying to do the problems you want to solve.Īnother issue will likely be trying to translate the abstract notation that makes perfect sense to you and everyone else who have been working for years on the kind of problems you are interested in into a notation that WolframAlpha is able to understand. For lots of years I think I remember that limit appeared to be about 80 characters, but it seems that the limit was increased to about 125 characters years ago. Part of the design decisions that went into WolframAlpha appear to have included a line length limit (at least for the free online version, I can't speak about the paid "pro" version of WolframAlpha), you can't enter a problem that takes 250 characters to input or that needs 250 characters in some intermediate or final step in doing the problem. I think WolframAlpha was originally intended to do "small" problems more easily for students than something like Wolfram Mathematica.
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