# MATLAB: How to create a loop for a constant value in a numerical integration problem and plot all solutions on the same graph

## MATLAB: How to create a loop for a constant value in a numerical integration problem and plot all solutions on the same graph

for loopintegrationnumerical integration

I have an .m-file that approximates the solution to a definite integral using Boole’s rule (numerical integration).
I have a definite integral I want to approximate, with respect to theta:
``f=@(theta) (1/pi)*cos(z*sin(theta)-5*(theta));``
The integral has a constant value, z, in it. I want the integral to be evaluated with z values from 0-25. When I run the code I want to obtain the values of approximation with the different z values, and I also want to plot the different z values. It should look something like the Bessel function.
I know I could obtain the values by changing the z value and running the code:
``f=@(theta) (1/pi)*cos(z*sin(theta)-5*(theta));a=0;b=pi;z=0;[r]=boole(f,a,b,n);disp (r);``
And then repeat the same process, only with z=1,2,3,…25.
`` f=@(theta) (1/pi)*cos(z*sin(theta)-5*(theta));  a=0;  b=pi;  z=1;  [r]=boole(f,a,b,n);disp (r); plot (r);``
Can I create a for loop with the constant z-value so when I run the code it gives all of the values of the approximation with z=0 to 25? Can I then group all of these values and plot them on one graph?
Any help would be much appreciated! Thanks 🙂

• ``f = @(theta) (1/pi)*cos(z*sin(theta)-5*(theta));%your other variablesz_vec = 0:25;for k=1:length(z)    z=z_vec(k); %pick the z for this iteration    [r{k}]=boole(f,a,b,n); %call your function    disp (r{k}); %disp results of this iteration    plot (r{k}); %plot    hold on end``