Floating-point scalars

I need to integrate the following with the given limits,

    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)]);
    max_zlimit=z0.*cos(phi);
    fun1=@(z) z*1/Lf;
    Q1=integral(fun1,0,max_zlimit);

Can someone please tell me how it can be done?

[jack carter]

even if i take

     max_zlimit=z0;

i still cant go through the integration

Answer 1

[Star Strider]

I am not certain what you want to do, so I’m taking my best guess at it.

This runs:

Lf=12;
E=22000;
rou=1.2;
d=0.039;
L=2;
N = 50;
v= linspace(0,Lf,N);
phi= linspace(0,pi/2,N);

s=v/(Lf/2);
z0=1-sqrt((E/rou)*(d/L)*s);
max_zlimit=z0.*cos(phi);
fun1=@(z) z*1/Lf;
Q1 = arrayfun(@(z)integral(@(z)fun1(z),0,z), max_zlimit);

The arrayfun function substitutes the values in ‘max_zlimit’ in your integral call, and returns the vector of results.

I defer to you to determine if it gives the output you want.

Answer 2

[John D'Errico]

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.

Q1 = max_zlimit.^2/24

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.

Q1 = max_zlimit.^2/24;

So Q1 is an array, the desired integral for all combinations of the two vectors.

size(Q1)
ans =
   201   158

By the way, integral is not designed to handle vector or array limits of integration anyway.