% numerical intergration
clear all 
close all

h=.1;
x=pi/2:h:2*pi;
y=sin(x);
figure(1)
plot(x,y)

% the trapz command- gives you the definite integral over the whole vector
yint=trapz(x,y);
 
% the cumtrapz command- gives you the integral as a vector of same length
% as x
yintcum=cumtrapz(x,y);
hold on
plot(x,yintcum,'r')

% the quad function -uses recursive Simpsons rule algorithm
% likes functions as inputs
a=8;
yint2=quad(inline('exp(x)'),-1,1);
%when using inline, always use x as the variable.

% using quad with a function call
for i=1:5
    newint(i)=quad(@(x)exponential(x,i),0,1);
end

% dblquad- double integration
[x,y]=meshgrid(-pi:.1:pi, -pi:.1:pi);
%x=-1:.05:1;
%y=-1:.05:1;
z=sincos(x,y); %function call using sincos.m, you can also use dblgauss.m
figure(2)
plot3(x,y,z)

gaussint=dblquad('sincos(x,y)',-1,1,-1,1);

%there is a triplequad