MATLAB: Trapz or integral which one is more accurate

integraltrapz

clc
clear
close all
x = linspace(0,100);
y = x.^cos(x);
plot(x,y);
a = trapz(x,y);
y = @(x)x.^cos(x);
b = integral(y,0,100);
c=a-b;

integral is more accurate here. Try

x = linspace(0,100,1000);

and you will find the trapz result reduces to get much closer to the integral result.

syms x
y=x^2
f=int(y,1,x) % integration between 1 and x

Notice you have:

fun= @(x, y) x.*exp(-y.*x);

which is a function of two variables. But you try

c= @(y)integral(@(x) fun, 0,1);

which does not pass any parameters to the function. You probably intended

c= @(y)integral(@(x) fun(x), 0,1);

But notice that you are not passing y, so you would need

c= @(y) integral(@(x) fun(x, y), 0,1);

Then you have

fun1= @(y) 1/2-(1/pi).*y.*c;
c1 = integral(fun1, 0,1);

this attempts to invoke c, but c is a function handle. You have to pass a value to the handle:

fun1 = @(y) 1/2-(1/pi).*y.*c(y);
c1 = integral(fun1, 0,1);

I think that should work.