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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