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Unformatted text preview: Homework 6 Lectures 2124 Math 344 Ohio University Spring Quarter 09’10’ Bob Benjamin Astrom Elbert Note: In the problems represented in this homework the percent error has values that are negative. The percent error is always positive however for some of the problems it is required to examine which direction (positive or negative) the error is. For this reason the absolute value has been removed from the percent error. 21.2) function [L R T] = myints(f,a,b,n) % Math 344 % Homework Problem 21.2 % Written by Astrom and Elbert % % Calculates the area under a function curve (integration) % using the Left and Right endpoint rules and the Trapezoid Rule % % inputs f, a, b and n % f is the function % a is the start point of integration % b is the end point of integration % n is number of intervals % The intervals have a start and end point which will % require n+1 points to make n intervals L = 0; % Set L to begin integration at 0 R = 0; % Set R to begin integration at 0 T = 0; % Set T to begin integration at 0 delta = (ba)/n; % Width of interval x = linspace(a,b,n+1); % Vector of n+1 points y = f(x); % Set function to variable y for i = 1:n % Loop to calculate area L=L+y(i)*delta; % Calculate using Left point R=R+y(i+1)*delta; % Calculate using Right point T=T+(y(i)+y(i+1))/2*delta; % Calculate using Trapezoid end % End calculation loop >> f = inline('sqrt(x)','x'); >> a = 1; >> b = 2; >> n = 4; >> [L R T] = myints(f,a,b,n) L = 1.166413628918445 R = 1.269967019511719 T = 1.218190324215082 >> n = 100; >> [L R T] = myints(f,a,b,n) L = 1.216879128301471 R = 1.221021263925201 T = 1.218950196113336 The percent error was calculated by adding a few extra lines of code on to the program. The extra code uses symbolic variables to calculate the definite integral with bounds “a” and “b” and then the percent error was calculated using the definite integral as the accepted value. function [L R T] = myintslong(f,a,b,n) % Math 344 % Homework Problem 21.2 % Written by Astrom and Elbert % % Calculates the area under a function curve (integration) % using the Left and Right endpoint rules and the Trapezoid Rule % as well as the percent error associated with each method % inputs f, a, b and n % f is the function % a is the start point of integration % b is the end point of integration % n is number of intervals % The intervals have a start and end point which will % require n+1 points to make n intervals format long L = 0; % Set L to begin integration at 0 R = 0; % Set R to begin integration at 0 T = 0; % Set T to begin integration at 0 delta = (ba)/n; % Width of interval x = linspace(a,b,n+1); % Vector of n+1 points y = f(x); % Set function to variable y for i = 1:n % Loop to calculate area L=L+y(i)*delta; % Calculate using Left point R=R+y(i+1)*delta; % Calculate using Right point T=T+(y(i)+y(i+1))/2*delta; % Calculate using Trapezoid end % End calculation loop syms x y % Allow x and y to be symbolic true = int(f(x),x,a,b); % Definite integral true answer...
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 Spring '08
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 Bob Benjamin Astrom Elbert

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