How to use the Simpson 1/3 rule to write this program

*To*: mathgroup at smc.vnet.net*Subject*: [mg76104] How to use the Simpson 1/3 rule to write this program*From*: Evanescence <origine26 at yahoo.com.tw>*Date*: Wed, 16 May 2007 05:33:30 -0400 (EDT)

Hello Dear all: My questions are as follows: First I have some functions are as follows: K[z_,x_] is a function of z and x. B[x_,y_] is a function of x and y. F[x_] is a function of x. Z[x_] is a function of x. A[x_,y_] is a function of x and y. G[x_] is a function of x. U[x_] is a function of x. Then I have a integration as follows: L[x_,y_,z_]:=(x*K[z,x])*(B[x,y]*F[x]*Z[x]+2*(A[x,y]-B[x,y]*G[x])*U[x]) L[x,y,z] integrate to x , and the upper limit is 32 , the lower limit is 0 So the integration form actually is a function of y and z. Now I want to use Simpson 1/3 rule to repreaent the integration , so the integration becomes as follows (Assume I use the division is 1/2) W[y_,z_]:=(1/3)*(32-0/64)*(0+4(((1/2)*K[z, 1/2])*(B[1/2,y]*F[1/2]*Z[1/2]+2*(A[1/2,y]-B[1/2,y]*G[1/2])*U[1/2]))+ 2(((1)*K[z,1])*(B[1,y]*F[1]*Z[1]+2*(A[1,y]- B[1,y]*G[1])*U[1]))+ 4(((3/2)*K[z, 3/2])*(B[3/2,y]*F[3/2]*Z[3/2]+2*(A[3/2,y]-B[3/2,y]*G[3/2])*U[3/2]))+ 2(((2)*K[z,2])*(B[2,y]*F[2]*Z[2]+2*(A[2,y]- B[2,y]*G[2])*U[2]))+ 4(((5/2)*K[z, 5/2])*(B[5/2,y]*F[5/2]*Z[5/2]+2*(A[5/2,y]-B[5/2,y]*G[5/2])*U[5/2]))+ ............................................................................................................. + 4(((63/2)*K[z, 63/2])*(B[63/2,y]*F[63/2]*Z[63/2]+2*(A[63/2,y]- B[63/2,y]*G[63/2])*U[63/2]))+ (((32)*K[z, 32])*(B[32,y]*F[32]*Z[32]+2*(A[32,y]-B[32,y]*G[32])*U[32]))) My question is how to writr a computer program to represent W[y_,z_] and I can set the upper limit ,the lower limit,and the division in myself. Thank you for your advice and answer!! Evanescence 2007 5 15.