Apply the composite Gaussian Quadrature to approximate the integralfo f(x)dx for a = 0, b = 1, f(x) = x² + 3x using N = 10 subintervals. Calculate the absolute error using the exact integral. Repeat your calculation for N = 10, 20, 30, 40, 50. Observe the error as N gets larger. Program Flow • Import necessary Python libraries • Define the integrand f(x) • Define a function for the single Qaussian Qudrature rule given the input variables ▪ left end point of interval ▪ right end pont of interval ▪ integrand f b-a • Determine the length of each subinterval h = N • Construct a partition of the integration domain [a, b] • For each subinterval ▪ calculate the approximate integral on subinteval [x₁-1 - x₂] ▪ add the result to all previous subintervals • Calculate the absolute error Display the final approximate integral and the absolute error
Apply the composite Gaussian Quadrature to approximate the integralfo f(x)dx for a = 0, b = 1, f(x) = x² + 3x using N = 10 subintervals. Calculate the absolute error using the exact integral. Repeat your calculation for N = 10, 20, 30, 40, 50. Observe the error as N gets larger. Program Flow • Import necessary Python libraries • Define the integrand f(x) • Define a function for the single Qaussian Qudrature rule given the input variables ▪ left end point of interval ▪ right end pont of interval ▪ integrand f b-a • Determine the length of each subinterval h = N • Construct a partition of the integration domain [a, b] • For each subinterval ▪ calculate the approximate integral on subinteval [x₁-1 - x₂] ▪ add the result to all previous subintervals • Calculate the absolute error Display the final approximate integral and the absolute error
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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Python
![Apply the composite Gaussian Quadrature to approximate the integral f f(x)dx for
a = 0, b = 1, f(x) = x² + 3x using N = 10 subintervals. Calculate the absolute error using
the exact integral. Repeat your calculation for N = 10, 20, 30, 40, 50. Observe the error as N
gets larger.
Program Flow
• Import necessary Python libraries
• Define the integrand f(x)
• Define a function for the single Qaussian Qudrature rule given the input variables
▪ left end point of interval
▪ right end pont of interval
▪ integrand f
b-a
N
• Construct a partition of the integration domain [a, b]
For each subinterval
Determine the length of each subinterval h
=
▪ calculate the approximate integral on subinteval [x₁-1 − x¡]
▪ add the result to all previous subintervals
• Calculate the absolute error
Display the final approximate integral and the absolute error](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa4aac48a-4d20-41e4-aba5-4ec9a336b2fd%2Fa24fae90-37e1-4abf-8707-2b432c2ec3e9%2Fymgwj5h_processed.png&w=3840&q=75)
Transcribed Image Text:Apply the composite Gaussian Quadrature to approximate the integral f f(x)dx for
a = 0, b = 1, f(x) = x² + 3x using N = 10 subintervals. Calculate the absolute error using
the exact integral. Repeat your calculation for N = 10, 20, 30, 40, 50. Observe the error as N
gets larger.
Program Flow
• Import necessary Python libraries
• Define the integrand f(x)
• Define a function for the single Qaussian Qudrature rule given the input variables
▪ left end point of interval
▪ right end pont of interval
▪ integrand f
b-a
N
• Construct a partition of the integration domain [a, b]
For each subinterval
Determine the length of each subinterval h
=
▪ calculate the approximate integral on subinteval [x₁-1 − x¡]
▪ add the result to all previous subintervals
• Calculate the absolute error
Display the final approximate integral and the absolute error
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