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, . .. , Xn, ..., XN. Each interval is Ax = (b – a)/N. The Simpon numerical integration rule is derived as: L. f(x)dx z 4* [f(xo) + 4 (E odd F(xn) + 2 (E even f(xn)) + f(xx)] . Zn=1. 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, don't change it). # 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
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, . .. , Xn, ..., XN. Each interval is Ax = (b – a)/N. The Simpon numerical integration rule is derived as: L. f(x)dx z 4* [f(xo) + 4 (E odd F(xn) + 2 (E even f(xn)) + f(xx)] . Zn=1. 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, don't change it). # 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
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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![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 Simpon numerical integration rule is derived as:
N-2
Li f(x)dx =
* f(x0) + 4 (2n odd f(xn)) + 2 ( En=2,n even
N-1
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, don't change it).
In [ ]: # 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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc4205fce-0b4d-4640-b3f9-45e32a33cf84%2F7972ff81-1625-45b7-a2e4-06a81393e6f0%2Flh9i4rm_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, ..., Xn,..., XN.
Each interval is Ax =
(b – a)/N.
The Simpon numerical integration rule is derived as:
N-2
Li f(x)dx =
* f(x0) + 4 (2n odd f(xn)) + 2 ( En=2,n even
N-1
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, don't change it).
In [ ]: # 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
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