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' );