how to use Simpson 1/3 with different area at different time-step

Hi Everyone,

I tried searching the web for a solution but could not get any solutions, so i hope anyone out there could help me. First of all I am new to matlab, so please pardon my bad coding style.

What I am trying to compute is a free-fall lifeboat buoyancy force which is = density*gravity*area. However, the height of the lifeboat will be different at different step, for example:

   X                        f(x)
  0                      1*3*2.3
  1.4166                 1*3*2.4
  2.8332                 1*3*2.5
  4.2498                 1*3*2.5
  5.6664                 1*3*3
  7.083                  1*3*3
  8.5                    1*3*3

At every single X there will be a different F(x) value which is the cross-section area of the lifeboat, and i need to do it for 40 segments, do you know how can i compute this? I tried as seen in the code attach, but i still having trouble at defining my function, could you help me take a look please?

Thank you

Best Regards

Noel

%INPUTS
L      = 0;   %lower limit
U      = 8.5; % upper limit
n      = 40;  % number of segments
Length = 1;
Breath = 3;
density= 1.025;
g      = 9.81;

func = @(Height) (Length * Breath * Height);
h = (U-L)/n;

st4 = 0;
st2 = 0;

for i = 2:h:n-1
    st4 = st4 + 4*func(i);
end

for i = 3:h:n
    st2 = st2 + 2*func(i);
end

I = (density*g)*(h/3*(func(1)+st4+st2+func(n)));