The Algorithms
The Trapezium Method
C
The trapezium rule is a way of estimating the area under a curve. We know that the area under a curve is given by integration, so the trapezium rule gives a method of estimating integrals.
Let's check this method for the next function: $$f(x) = ({e^x / 2})*(cos(x)-sin(x))$$ with $\varepsilon = 0.001$
import math
import numpy as np
n = 4
a = 2.
b = 3.
def f(x):
return (math.e**x / 2)*(math.cos(x)-math.sin(x))
def trapezoid(a,b,n):
z = (b-a)/n
i=a
s=0
while (i+z)<b:
s=s+f(i)
i=i+z
s=z*(f(a)+f(b))/2+s
print('Result: ',s)
trapezoid(a,b,n)Result: -22.12539445092147
