Tell the truth, work hard, and come to dinner on time.
Gerald R. Ford
And they called that fellow stupid... He knows the secret of life and they do not and he is stupid...?
Bet I could have made a good EM guy out of him.
Represent the 3 points by A(x1,1/x1), B(x2,1/x2), and C(x3,1/x3). Translate the triangle with C at the origin. Then use the formula given here for G.
Plug in A and B, this computes the orthocenter of ABC'. Translate that back using the translation done on C.
Laborious algebra? ( get Wolfram Alpha to help you if you need that )
You will end up with an orthocenter at (-1/(x1*x2*x3), -x1*x2*x3). Clearly this is on the curve xy=1 and we are done.
The purpose of math is to eliminate the need for intelligent thought
When all else fails work like a computer would, you have the time. Never leave a question blank on a test or at work. Took me 3 hours to eat this turkey. At least I have something to hand in, something of my own, something that professor is gonna have to think about and in the end at least give me some partial credit. That few points may mean the difference between passing or not.
I am getting an error almost as big as the answer with other messages about slow convergence. There is no reliability in that answer at all.
We have talked quite a bit about lots of stuff. I do not care about your physical appearance, your gender, your religion, your social status or how much money you have. I only know you from your writings, so in the truest sense I consider you a friend. So as your friend I would like to offer some advice:
Here is a quote from someone over at Mathematica.SE for an integral that is not as complex as yours.
You have lots of stuff in the integral that does not depend on x. You should first manually reduce the complexity of the integrand and the number of variables to the minimum possible. And then you need to use assumptions for all remaining parameters since the integral most likely does not converge for arbitrary complex values of the parameters. Even then it might not work, but in the way you write it even much simpler integrals would not give a result.
It is the job of the human to prepare the problem for M to solve. That is our job now. Mathematica can not do the impossible. I have watched you suffering over these type of multiple integrals for months with little progress being made. I know you can make progress when the problem allows it. This type of problem is not amenable to progress either by you or M or anybody on any forum we have tried. It does look like this is a dead end.
Now I ask you, can you shorten that to no more than a double integral with very few unrelated parameters? These are the types M can do, these are the only types anyone can do. Unless your supervisor is willing to give out a lot more information about this problem then maybe it is time to abandon this and look for something else. What have you got to lose? Please think about this.
"Jayne has 3 quarters, 2 dimes, a nickel, and 2 pennies in her pocket. How many different amounts can she make using some or all of these coins?" Please solve this and show me how you got the answer step-by-step.
Use generating functions:
But we need to use some of the coins so 0 is out. There are 71 ways to give change using these coins but only 62 of them are different amounts so that is the answer.
I am not an expert on any of those and it is one of the reasons I stay away from 3D+.
To get useful ideas about any integration problem one has to look at the graph. Then it will be clear how to proceed. Take my integral as an example:
It is extremely tough but because I can graph the integrand I can gain insight into possble methods to deal with it. Yours is a 4 dimensional integral. I have never seen a 4D graph in our physical reality. The standard methods they teach in school are very weak. Even if we get a MCM working it will be very computationally intensive and will only yield 2 decimal places or so. This may not be enough to determine convergence.
Let me see what can be done and I will post my conclusions.