The Trapezium Method

C
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"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."
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"Let's check this method for the next function: $$f(x) = ({e^x / 2})*(cos(x)-sin(x))$$ with $\\varepsilon = 0.001$"
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"Result:  -22.12539445092147\n"
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"source": [
"import math \n",
"import numpy as np\n",
"\n",
"n = 4 \n",
"a = 2.\n",
"b = 3.\n",
"def f(x):\n",
"    return  (math.e**x / 2)*(math.cos(x)-math.sin(x))\n",
"\n",
"def trapezoid(a,b,n):\n",
"  z = (b-a)/n\n",
"  i=a\n",
"  s=0\n",
"  while (i+z)<b:\n",
"    s=s+f(i)\n",
"    i=i+z \n",
"  s=z*(f(a)+f(b))/2+s\n",
"  print('Result: ',s)\n",
"    \n",
"trapezoid(a,b,n)"
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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)&lt;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