#coding = utf-8
#simpson 法计算积分，数值积分，效果非常理想
from math import *
def func(x): 
 """
 定义被积分函数
 """
 return x*sin(x)
def Get_N(a,b,width):
 # width为步长
 N=int((b-a)/width + 1)
 if N%2 == 0:
  N=N+1
 return N
def GenerateData(a,b,n,width):
 datas = []
 r=a
 for i in range(0,n):
  datas.append(func(r))
  r = r+width
 return datas
def simpson_integral(datas,width,n):
 sum = datas[0]+datas[n-1]
 for i in range(2,n):
  if i%2== 0:
   sum = sum +4*datas[i-1]
  else:
   sum = sum +2*datas[i-1]
 return sum*width/3.0
if __name__ == "__main__":
 a=1.0 #积分上限
 b=3.0 #积分下限
 width=0.0625 #步长
 N=Get_N(a,b,width)
 datas = GenerateData(a,b,N,width)
 print simpson_integral(datas,width,N)