Re: a problem with integrate

*To*: mathgroup at smc.vnet.net*Subject*: [mg72678] Re: a problem with integrate*From*: Peter Pein <petsie at dordos.net>*Date*: Mon, 15 Jan 2007 04:51:19 -0500 (EST)*References*: <eocsb3$6st$1@smc.vnet.net>

starryin schrieb: > hello everyone,i'm a student in China.i meet with a problem when i > using mathematica to do this expression > > ?[x0_, y0_, y1_, z1_] := N[(1/10)*Sqrt[x0^2 + (y1 - y0)^2 + > z1^2]*(Abs[y1 - y0]/x0 + 1)] > f[y_, z_, y1_, z1_, x0_, y0_] := N[1/((2*Pi*?[x0, y0, y1, > z1]^2)*N[e^(((y - y1)^2 + (z - z1)^2)/(2*?[x0, y0, y1, z1]^2))]),5] > D1[x0_, y0_] := NIntegrate[f[y, z, y1, z1, x0, y0], {z1, 0, 2.44}, {y1, > 0, 69}, {z, 0, 2.44}, {y, 30.84, 34.5}] > > after i define the function ,i input D1[3,5] to get one answer ,but i > got a warning message: > > Integrand epr(i can not paste the expression here) is not numerical at > {z1, y1, z, y}= {1.22`, 34.5`, 1.22`, 32.67'}. > > who can tell me how can i solve the problem? do i need to use Integrate > instead of NIntegrate? or do i need to add some other parameter ? > i' m so sorry that my english is not good enough to express my question > ?but i still wish some one can solve my problem > thanks! > Hi, 1.) your variable "e" is undefined. I _guess_ you wanted "E" instead. 2.) there is no need to use N[..] inside your functions, but it should not do too much harm (I didn't investigate this point further). NIntegrate[] works already with inexact numbers. 3.) In this case, NIntegrate gives a fast result, when using the option Method->Multidimensional. After replacing the unreadable functionname by "g", I get the following: In[1]:= g[x0_, y0_, y1_, z1_] := (1/10)*Sqrt[x0^2 + (y1 - y0)^2 + z1^2]*(Abs[y1 - y0]/x0 + 1); f[y_, z_, y1_, z1_, x0_, y0_] := 1/((2*Pi*g[x0, y0, y1, z1]^2)* E^(((y - y1)^2 + (z - z1)^2)/(2*g[x0, y0, y1, z1]^2))); D1[x0_, y0_] := NIntegrate[f[y, z, y1, z1, x0, y0], {z1, 0, 61/25}, {y1, 0, 69}, {z, 0, 61/25}, {y, 771/25, 69/2}, Method -> MultiDimensional]; D1[3,5]//Timing Out[4]= {0.031 Second,0.209833} Is this result inside the expected range? Cheers, Peter