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 = xo.x1.x2. XXN. Each interval is A.x = (b-a)/N. The equation for the Simpson numerical integration rule is derived as: f(x)dx= [(xo) + 4 (Elodd S(x)) + 2 (E2²even S(x))+S(XN)]. 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 f(x) = 2x³ (Already defined in the function, no need to change). *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): as 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- # 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, b))
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 = xo.x1.x2. XXN. Each interval is A.x = (b-a)/N. The equation for the Simpson numerical integration rule is derived as: f(x)dx= [(xo) + 4 (Elodd S(x)) + 2 (E2²even S(x))+S(XN)]. 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 f(x) = 2x³ (Already defined in the function, no need to change). *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): as 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- # 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, b))
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
Related questions
Question
![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,..., X., XN. Each interval is Ax = (b − a)/N.
The equation for the Simpson numerical integration rule is derived as:
f f(x)dx ≈
[ƒ(x0) + 4 (EN-1,n odd S(x)) + 2 (Σ2²n even f(x)) + f(XN)].
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 f(x) = 2x³ (Already defined in the function, no need to change).
*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, b))](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F95b5a871-62fa-479b-89b7-393477eed51e%2F4fc42ee7-1f12-4f2e-9416-e1d384ba2b07%2Fi2fhb1_processed.png&w=3840&q=75)
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,..., X., XN. Each interval is Ax = (b − a)/N.
The equation for the Simpson numerical integration rule is derived as:
f f(x)dx ≈
[ƒ(x0) + 4 (EN-1,n odd S(x)) + 2 (Σ2²n even f(x)) + f(XN)].
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 f(x) = 2x³ (Already defined in the function, no need to change).
*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, b))
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Computer Networking: A Top-Down Approach (7th Edi…
Computer Engineering
ISBN:
9780133594140
Author:
James Kurose, Keith Ross
Publisher:
PEARSON
Computer Organization and Design MIPS Edition, Fi…
Computer Engineering
ISBN:
9780124077263
Author:
David A. Patterson, John L. Hennessy
Publisher:
Elsevier Science
Network+ Guide to Networks (MindTap Course List)
Computer Engineering
ISBN:
9781337569330
Author:
Jill West, Tamara Dean, Jean Andrews
Publisher:
Cengage Learning
Computer Networking: A Top-Down Approach (7th Edi…
Computer Engineering
ISBN:
9780133594140
Author:
James Kurose, Keith Ross
Publisher:
PEARSON
Computer Organization and Design MIPS Edition, Fi…
Computer Engineering
ISBN:
9780124077263
Author:
David A. Patterson, John L. Hennessy
Publisher:
Elsevier Science
Network+ Guide to Networks (MindTap Course List)
Computer Engineering
ISBN:
9781337569330
Author:
Jill West, Tamara Dean, Jean Andrews
Publisher:
Cengage Learning
Concepts of Database Management
Computer Engineering
ISBN:
9781337093422
Author:
Joy L. Starks, Philip J. Pratt, Mary Z. Last
Publisher:
Cengage Learning
Prelude to Programming
Computer Engineering
ISBN:
9780133750423
Author:
VENIT, Stewart
Publisher:
Pearson Education
Sc Business Data Communications and Networking, T…
Computer Engineering
ISBN:
9781119368830
Author:
FITZGERALD
Publisher:
WILEY