MATLAB/Cookbook/symbolicIntegration

clc;clear all;close all
sectionNumber= input('Enter case you wish to run: ');
switch(sectionNumber)
    case 1
        syms x  real %certain matlab commands don't need semicolon to suppress output
        syms a b positive
        f=a*x^3*exp(-b*x^2) %symbolically define function to be intetrated
        int_f=int(f,x) % *int* integrates f w.r.t. x and shows result
        pretty(int_f); %makes result easier to read
        
    case 2
        syms x  real, syms a b positive 
        f=a*x^3*exp(-b*x^2); %symbolically define function to be intetrated
        int_f=int(f,x,0) % constant of integration allows int_f(0)=0
        pretty(int_f); %makes result easier to read
    
    case 3
        syms x  real %Here we introduce ezplot, which plots symbolic 
        % functions, but lacks the options available with plot.
        f=x^3*exp(-x^2); 
        int_f=int(f,x) 
        ezplot(f,[0,3])
        title('function (first of two figures)')
        % ezplot almost forces us to put the integral on a separate plot.
        figure 
        ezplot(int_f,[0,3])
        title('integral (second of two figures)')
    case 4
        syms x x1 x2 real
        syms a b positive
        f=x^3*exp(-1*x^2);
        int_f=int(f,x,0);
        xplot=0:.01:3;
        % the next two commands convert symbols to double precision numbers
        fplot = double(subs(f, x, xplot));
        Sfplot = double(subs(int_f, x, xplot));
        plot(xplot, fplot, 'b', xplot, Sfplot, 'r-.');
        title(' ');
        legend('function','integral');
        xlabel('x'); grid;
end
        fprintf('To run this code again type *symbolicIntegration*\n' );