sympyで「Python - 数値積分 台形法 & シンプソン法」を参考にした

(参考)Python - 数値積分 台形法 & シンプソン法
http://qiita.com/popondeli/items/fbc602b80223227f3d0e

from sympy import *
var("x a b")
f=x**5
print(integrate(f))
print(integrate(f, (x, a, b)))
a=0
b=2
print(integrate(f, (x, a, b)))
print(float(integrate(x**5, (xx**6/6

# x**6/6
# -a**6/6 + b**6/6
# 32/3
# 10.666666666666666

(参考)Wolfram|Alpha: Computational Knowledge Engine＞int(x^5)
http://www.wolframalpha.com/input/?i=int(x%5E5)
x^6/6
(参考)Wolfram|Alpha: Computational Knowledge Engine＞Integrate[x^5, {x, 0, 2}]
http://www.wolframalpha.com/input/?i=Integrate%5Bx%5E5,+%7Bx,+0,+2%7D%5D
integral_0^2 x^5 dx = 32/3≈10.667