integration problem ..not directly applicable ..not easy too

[ysenthilece]

x1+x2+x3=1 && x1+x2>x3 && x2+x3>x1 && x1+x3>x2

i need the total number of points satisfying all the above conditions (quantified as area formed )

this could be solved easily by using analytical geometry ...


but i need to generalise this for the case n variables of x..so i can't visualise and do ..

so is there some procedure to do the above problem so tat i could generalise it for the case n .

ie x1+x2+.....+xn=1 && x1+x2...........x(n-1)>xn .....so on

for n=4 it is a volume ...which could be calculated too with some difficulty....but i need for any n...

 

[VSMVDD]

Re: integration problem ..not directly applicable ..not easy

sounds like a problem set by a teacher

my advice is not to use n factors

as this is an additive progression only

so n =1/x + 1/2x.... etc

as it is all calculated over 1 you then only need

to divide your 1/x{finaly x value} value by 100/n

 

[steve10]

Re: integration problem ..not directly applicable ..not easy

Here you go but .... you need to make up the details.

 

[steve10]

Re: integration problem ..not directly applicable ..not easy

Just wanna assue you that the matrix B is easy to get. Actually, B consists of only two numbers in the whole matrix, just like that the matrix A consists of two numbers which are 1 and -1. On the diagonal of B, the element is -(n-3)/(2(n-2)) while it is 1/(2(n-2)) everywhere else. Again, you may wanna check AB=I, which is the unit matrix.

 

[eda_freak]

Re: integration problem ..not directly applicable ..not easy

Hey,

i have seen the solution to this problem by somebody on this forum...
just lookout for that post...