Question

Problem 3. Consider the running integral T dx 0x3 0 Determine: (a) the exact value over the domain, (b) the zero-order approximation, and c) the zero-order approximation. Apply 100 points on the interval 0xs3. (d) Plot the approximation as a continuous curve and the exact value as a sequence of o's Q8. What is exact value of z for 0<x<3 ? Q9. What is approximate value of z for 0sx<3 when using zero-order approximation with 100 points over domain? Q10. What is approximate value of z for 0sx3 when using first-order approximation with 100 points over domain? USE MATLAB

Answer 1

solution;

clc;
clear all;
y=linspace(0,3,100); %y is input
z=zeros(1,100);
syms x;
%a)
fun= x*exp(-(x^2));
for i=1:100
C= int(fun,0,y(i));
z(i)=vpa(C);
end   
% z is exact value

%b) zero order approximation (zoa)
zoa=mean(z);

%c) first order approximation (foa)
P=polyfit(y,z,1);
%P(1) is slope and P(2) is constant term:::P(1)x+P(2)
%d) plot
plot(y,z,'ro');
hold on;
plot(y,z);