#Trapezoidal rule
# โจทย์ f(x) = e^x*sin(x) ,n=10
from math import e,sin
def f(x) :
    return e**x*sin(x)
#n คือ จำนวนกรแบ่งช่วง
#h คือ ค่าของช่วงที่แบ่ง from (b-a)/n
def trap(f,a,h,n) :
    return sum([ (1/2)*h*(f(a+i*h)+f(a+(i+1)*h)) for i in range(n) ])
def area(f,a,b,n):
    return sum([ (1/2)*((b-a)/n)*(f(a+i*((b-a)/n))+f(a+(i+1)*((b-a)/n))) for i in range(n) ])
trap(f,0.1,0.05,10),area(f,0.1,0.6,10)

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#หา integrate จาก Sympy
x,y=sympy.Symbol('x'),sympy.Symbol('y')
y=3*x**2+9*x+2
z=sympy.integrate(y,(x,0.1,0.6))
from math import e
zz = e**-x
zzz = sympy.integrate(zz,(x,0,1))
y,z,zzz

#Simpson's rule

import sympy
from math import e
f =e**(-x)
sympy.integrate(f,(x,0,1))

#print 0.632120558828558

def simpson(f, a, b, n):
    h = (b-a)/n
    x0 = a # x_i = x_0 + i*h
    #f(x0) + 4*f(x1) + 2*f(x2) + .... + 4*f(x_n-1) + f(x_n)
    s = f(x0)
    
    # odd - x1, x3, x5, ... 
    #s += 4*f(x1) + 4*f(x3) + 4*f(x5) + ...
    for i in range(1,n,2):
        s += 4*f(x0+i*h)
        
    # even - x2, x4, x6, ...
    #s += 2*f(x2) + 2*f(x4) + 2*f(x6) + ...
    for i in range(2,n-1,2):
        s += 2*f(x0+i*h)
    
    s += f(x0+n*h)
    return s*h/3

from math import e
from sympy import *
def f(x): return e**(-x)
a,b = 0,1
r=0.632120558828558
simpson(f, a, b, 4)
for v in [ (n,simpson(f,a,b,n),area(f,a,b,n)) for n in range(4, 22, 2) ] :
    print ('{:5} {:20} {:20}'.format(v[0],abs(v[1]-r),v[2]))