In [24]:
from sympy import *
In [34]:
x, x_i, h = symbols('x x_i h')
init_printing(use_latex='mathjax')
In [43]:
expr1 = ((x-x_i+h)/h)**2
expr2 = ((x_i+h-x)/h)**2
result = integrate(expr1, (x, x_i-h, x_i))+integrate(expr2, (x, x_i, x_i+h))
simplify(result)
Out[43]:
$\displaystyle \frac{2 h}{3}$
In [44]:
expr = (x_i+h-x)*(x-x_i)/(h**2)
result = integrate(expr, (x, x_i, x_i+h))
simplify(result)
Out[44]:
$\displaystyle \frac{h}{6}$
In [45]:
expr = (x_i-x)*(x-(x_i-h))/(h**2)
result = integrate(expr, (x, x_i-h, x_i))
simplify(result)
Out[45]:
$\displaystyle \frac{h}{6}$