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 A.x, 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 [f(x) + 4 (Emln odd f(x)) + 2 (E-2n even f(x)) + f(x)]. 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).
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 A.x, 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 [f(x) + 4 (Emln odd f(x)) + 2 (E-2n even f(x)) + f(x)]. 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).
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
Related questions
Question
![Markdown
Validate
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"""
$
ܠ
def f(x):
## The function f(x)=2*x**3 is defined as below, DON'T CHANGE IT:
f=2*x**3
return f
return TotalArea
####Check your code by using print command below###
| Idle Mem: 262.63/12288.00 MB
N=100
a=1
b=3
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
print (InterageSimpson (N, a, b))
[ ]: ## Don't write any code in this box
[ ]: ## Don't write any code in this box
[ ]: ## Don't write any code in this box
[ ]: ## Don't write any code in this box
Q
R
F4
FL
%
5
g
F5
T
G
^
6
# Make sure in your solution, you use the same name "TotalArea" for the output
F6
Y
H
&
7
F7
U
* 0
8
Mode: Command
DII
F8
(
9
K
X
DD
F9
Ln 1, Col 1 English (United States) Python_coursework.ipynb
)
0
J
A
F10
0 P
I
4
5
F11
0 Python 3 (pyk
{
[
11
4)
F12
}
]
E](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F226fee03-c629-4185-8cef-0e29840a7a8d%2Fb7c96376-fc71-4953-8b35-d8a13ee9ea78%2Fplthyp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Markdown
Validate
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"""
$
ܠ
def f(x):
## The function f(x)=2*x**3 is defined as below, DON'T CHANGE IT:
f=2*x**3
return f
return TotalArea
####Check your code by using print command below###
| Idle Mem: 262.63/12288.00 MB
N=100
a=1
b=3
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
print (InterageSimpson (N, a, b))
[ ]: ## Don't write any code in this box
[ ]: ## Don't write any code in this box
[ ]: ## Don't write any code in this box
[ ]: ## Don't write any code in this box
Q
R
F4
FL
%
5
g
F5
T
G
^
6
# Make sure in your solution, you use the same name "TotalArea" for the output
F6
Y
H
&
7
F7
U
* 0
8
Mode: Command
DII
F8
(
9
K
X
DD
F9
Ln 1, Col 1 English (United States) Python_coursework.ipynb
)
0
J
A
F10
0 P
I
4
5
F11
0 Python 3 (pyk
{
[
11
4)
F12
}
]
E
![-
Python 3 (pyke
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:
df(xn)) + 2 (Σ=2n 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 f(x) = 2x³ (Already defined in the function, no need to change).
Sof(x)dx≈ [f(x) + 4 (N=
[]: '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"
a
Idle Mem: 262.63/12288.00 MB
F4
R
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"""
LL
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###
%
5
9
F5
n=1,n odd -
T
G
6
C
F6
Y
H
&
F7
f(x₂)) + f(xN)].
U
*
8
Mode: Command Ⓡ
DII
F8
K
(
9
F9
0
Ln 1, Col 1 English (United States) Python_coursework.ipynb
)
O
♫
F10
P
:
4
F11
{
+ 11
11
F12
}
1
E](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F226fee03-c629-4185-8cef-0e29840a7a8d%2Fb7c96376-fc71-4953-8b35-d8a13ee9ea78%2Fghaxqrh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:-
Python 3 (pyke
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:
df(xn)) + 2 (Σ=2n 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 f(x) = 2x³ (Already defined in the function, no need to change).
Sof(x)dx≈ [f(x) + 4 (N=
[]: '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"
a
Idle Mem: 262.63/12288.00 MB
F4
R
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"""
LL
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###
%
5
9
F5
n=1,n odd -
T
G
6
C
F6
Y
H
&
F7
f(x₂)) + f(xN)].
U
*
8
Mode: Command Ⓡ
DII
F8
K
(
9
F9
0
Ln 1, Col 1 English (United States) Python_coursework.ipynb
)
O
♫
F10
P
:
4
F11
{
+ 11
11
F12
}
1
E
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