Error in using Integration, How to fix it ?

I am trying to plot a function with integration in it, and it always gives me an error in using the integral, I tried using function handle for the first argument (according to the error) , but the error remaind.

t   = 0:0.02:20;
y   = 0:1000;
x   = @(t,y) (y/((4*t*0.02/1000)^0.5));

fun = @(x)(exp(-x.^2));
erf = (2/pi^(0.5))  *integral(fun,0,x);     % the error is in this line

erfc= 1 - erf;
VProfile= 10*erfc;
plot(t,VProfile)
title('Velocity Profile')
xlabel('time (sec)')
ylabel('Velocity (cm/sec)')

so what did I do wrong? and how can I fix it ? and if the code has another error I didnt notice, please point it out.

thank you.

Answer 1

[Alan Stevens]

Since x has t in the denominator. t=0 will cause problems, so start at t = 0.02 instead, perhaps! This would require a change in y to get the same number of elements as t.

You don't need x as a function. Replace with

x   = y./((4*t*0.02/1000).^0.5);

then calculate your error function in a loop:

for i = 1:numel(t)
    erf(i) = (2/pi^(0.5))*integral(fun,0,x(i)); 
end

Best not to use erf and erfc as they are functions already built-in to MATLAB. Better as, say, erF and erFc.