Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN: 9780133594140
Author: James Kurose, Keith Ross
Publisher: PEARSON
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"""Complete the function given the variables
N, a,b and return the value as "TotalArea". '
"Don't change the predefined content' only
fill your code in the region 'YOUR CODE'""""
from math import *
def InterageSimpson (N, a, b): # n is the total intervals, a and b is the lower and upper bound respectively
"""Hint: Use loop to add all the values
in the above equation and
use the if statement to determine
whether the value is odd or even""""
def f(x):
## The function f(x)=2*x**3 is defined as below, DON'T CHANGE IT:
f=2*x**3
return f
value=0 # Initial value
TotalArea=0 # TotalArea as the final integral value, the area underneath the curve.
dx=(b-a)/N # delta x, the interval length
# Complete the function by filling your codes below:
# YOUR CODE HERE
return TotalArea # Make sure in your
#solution, you use the same name "TotalArea" for the output
####Check your code by using print command below###
N=100
a=1
b=3
print (InterageSimpson (N, a,
四个↓ 古
b))
0+
expand button
Transcribed Image Text:"""Complete the function given the variables N, a,b and return the value as "TotalArea". ' "Don't change the predefined content' only fill your code in the region 'YOUR CODE'"""" from math import * def InterageSimpson (N, a, b): # n is the total intervals, a and b is the lower and upper bound respectively """Hint: Use loop to add all the values in the above equation and use the if statement to determine whether the value is odd or even"""" def f(x): ## The function f(x)=2*x**3 is defined as below, DON'T CHANGE IT: f=2*x**3 return f value=0 # Initial value TotalArea=0 # TotalArea as the final integral value, the area underneath the curve. dx=(b-a)/N # delta x, the interval length # Complete the function by filling your codes below: # YOUR CODE HERE return TotalArea # Make sure in your #solution, you use the same name "TotalArea" for the output ####Check your code by using print command below### N=100 a=1 b=3 print (InterageSimpson (N, a, 四个↓ 古 b)) 0+
We have learned the mid-point and trapezoidal rule for
numercial intergration in the tutorials. Now you are asked to
implement the Simpson rule, where we approximate the
integration of a non-linear curve using piecewise quadratic
functions.
Assume f(x) is continuous over [a, b] . Let [a, b] be
divided into N subintervals, each of length Ax, with
endpoints at P = x0, x1, x2,..
Xn,..., XN. Each
interval is Ax = (b − a)/N.
The equation for the Simpson numerical integration rule is
derived as:
f f(x) dx
N-1
Ax [ƒ(x0) + 4 (Σ1,n odd f(xn))
ƒ(x₂)) + f(xx)].
N-2
+ 2 (n=2,n even
Now complete the Python function InterageSimpson (N, a,
b) below to implement this Simpson rule using the above
equation.
The function to be intergrate is ƒ(x) = 2x³ (Already
defined in the function, no need to change).
expand button
Transcribed Image Text:We have learned the mid-point and trapezoidal rule for numercial intergration in the tutorials. Now you are asked to implement the Simpson rule, where we approximate the integration of a non-linear curve using piecewise quadratic functions. Assume f(x) is continuous over [a, b] . Let [a, b] be divided into N subintervals, each of length Ax, with endpoints at P = x0, x1, x2,.. Xn,..., XN. Each interval is Ax = (b − a)/N. The equation for the Simpson numerical integration rule is derived as: f f(x) dx N-1 Ax [ƒ(x0) + 4 (Σ1,n odd f(xn)) ƒ(x₂)) + f(xx)]. N-2 + 2 (n=2,n even Now complete the Python function InterageSimpson (N, a, b) below to implement this Simpson rule using the above equation. The function to be intergrate is ƒ(x) = 2x³ (Already defined in the function, no need to change).
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