Um, lets be serious. You are trying to integrate the "function" z/Lf, over simple limits. Lf is 12. With limits of 0 and max_zlimit, the integral is trivial.
Your problem is that what you want to do is not clear. Since v and phi have different lengths as a vector, I'll guess that what you want is all combinations of those two vectors as the upper limit.
Lf=12;E=22000;rou=1.2;d=0.039;L=2;v=0:0.01:L;phi=0:0.01:pi/2;
s=v/(Lf/2);
z0=1-sqrt([(E/rou)*(d/L)*(s)]);
We can get the array (thus all combinations of the two vectors) using a simple outer product.
max_zlimit=(z0.')*cos(phi);
So now the integral is trivial. We need never bother using a numerical integration scheme like integral.
So Q1 is an array, the desired integral for all combinations of the two vectors.
By the way, integral is not designed to handle vector or array limits of integration anyway.