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(Numerical Integration) Suppose we are given a function f(x) whose integral is not known explicitly. We may, however, wish to still approximate the value of the definite integral of f over the interval [a, b]. In order to do this, we could use the so-called composite trapezoid rule with n+1 nodes given by T-1 h Ls(2) dz = (s(a) + 2 fla + kh) + f(b)). k=1 where h = b-a comp_trap_rule Function: Input variables: • an anonymous function representing f • a scalar representing the lower bound of integration a • a scalar representing the upper bound of integration b • a scalar representing the value of n; you may assume this is an integer greater than 0 Output variables: • a scalar represcnting the approximate integral computed by the formula above A possible sample case is: » int = comp_trap_rule(@(x) x^2, 0, 1, 100) int 0.33335 %3!

(Numerical Integration) Suppose we are given a function f(x) whose integral is not known explicitly. We may, however, wish to still approximate the value of the definite integral of f over the interval [a, b]. In order to do this, we could use the so-called composite trapezoid rule with n+1 nodes given by T-1 h Ls(2) dz = (s(a) + 2 fla + kh) + f(b)). k=1 where h = b-a comp_trap_rule Function: Input variables: • an anonymous function representing f • a scalar representing the lower bound of integration a • a scalar representing the upper bound of integration b • a scalar representing the value of n; you may assume this is an integer greater than 0 Output variables: • a scalar represcnting the approximate integral computed by the formula above A possible sample case is: » int = comp_trap_rule(@(x) x^2, 0, 1, 100) int 0.33335 %3!

Database System Concepts
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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(Numerical Integration) Suppose we are given a function f(x) whose integral is not known explicitly. We may, however, wish to still approximate the value of the definite integral of f over the interval [a, b). In order to do this, we could use the so-called composite trapezoid rule with n+1 nodes given by h n-1 [S(2) dzx = (5(a) +2E f(a + kh) +, +2Ef(a + kh) + f(b k=1 where h = b-a comp_trap_rule Function: Input variables: • an anonymous function representing f • a scalar representing the lower bound of integration a • a scalar representing the upper bound of integration b • a scalar representing the value of n; you may assune this is an integer greater than 0 Output variables: • a scalar representing the approximate integral computed by the formula above A possible sample case is: > int = comp_trap_rule(@(x) x^2, 0, 1, 100) int = 0.33335
Transcribed Image Text:(Numerical Integration) Suppose we are given a function f(x) whose integral is not known explicitly. We may, however, wish to still approximate the value of the definite integral of f over the interval [a, b). In order to do this, we could use the so-called composite trapezoid rule with n+1 nodes given by h n-1 [S(2) dzx = (5(a) +2E f(a + kh) +, +2Ef(a + kh) + f(b k=1 where h = b-a comp_trap_rule Function: Input variables: • an anonymous function representing f • a scalar representing the lower bound of integration a • a scalar representing the upper bound of integration b • a scalar representing the value of n; you may assune this is an integer greater than 0 Output variables: • a scalar representing the approximate integral computed by the formula above A possible sample case is: > int = comp_trap_rule(@(x) x^2, 0, 1, 100) int = 0.33335
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