We can easily improve the formula by approximating the area under the function f(x) by two equally-spaced trapezoids. Derive a formula for this approximation and implement it in a function trapezint2( f,a,b ).

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ajeigbeibraheem ajeigbeibraheem · Answer 1 · 2021-03-09T19:18:15+01:00

Answer:

Explanation:

[tex]\text{This is a math function that is integrated using a trapezoidal rule } \\ \\[/tex]

[tex]\text{import math}[/tex]

def [tex]\text{trapezint2(f,a,b):}[/tex]

[tex]\text{midPoint=(a+b)/2}[/tex]

[tex]\text{return .5*((midPoint-a)*(f(a)+f(midPoint))+(b-midPoint)*(f(b)+f(midPoint)))}[/tex]

[tex]\text{trapezint2(math.sin,0,.5*math.pi)}[/tex]

[tex]0.9480594489685199[/tex]

[tex]trapezint2(abs,-1,1)[/tex]

[tex]1.0[/tex]

lhmarianateixeira lhmarianateixeira · Answer 2 · 2022-02-24T12:09:15+01:00

In this exercise we have to use the knowledge of computational language in python to write the code.

the code can be found in the attachment.

In this way we have that the code in python can be written as:

h = (b-a)/float(n)

s = 0.5*(f(a) + f(b))

for i in range(1,n,1):

s = s + f(a + i*h)

return h*s

from math import exp # or from math import *

def g(t):

return exp(-t**4)

a = -2; b = 2

n = 1000

result = Trapezoidal(g, a, b, n)

print result

See more about python at brainly.com/question/26104476