how to do it using matlab.

I have been asked to area averaging using scientific formula. The formula looks like this

      Let  A =      integral between limits[a b] [ f(x).dx ]    
                             My formula is 
                            B = 1/b *(A);
My main problem is f(x) is just set of data and hence not an equation. If it was simple/complicated equation I would have solved it. But since its data of time along x-axis & pressure along y-axis
pressure  916.3  923.6  933.1  947.4  966.2  986.6  1008.5  1031.5  1051.3
time  1  2  3  4  5  6  7  8  9

So I applied trapezoidal rule.. tried coding it. Got it for h=4(or integer) but h changes to some non integer value its throwing error. h=(b-a)/n, eg :n= 4, h = 1.3 Hence A1(2.3). Matlab doesn’t work with these kind of indices.. I want to read A1(23) when it means 2.3. Anyone can give me some help… //just tried

   t = 1:9;

   t1 = 1 : 0.1 :9;

   A = [916.3, 923.6, 933.1, 947.4, 966.2, 986.6, 1008.5, 1031.5, 1051.3];

   A1 = interp1(t ,A , t1) ;

   a= 1;

   b=9;

   h= 1.3;

   for i = 0:3

   res = 0.5*[A1(a+ i*h)+ A1(a + (i+1)*h)]*h

   disp(res)

   end

Answer 1

[ES]

I think I understand your question. trapz is a numerical integration method to which you supply a set of discontinued numbers. trapz will form trapezoids by interpolation, find the area under the curve. Look here<http://www.mathworks.in/help/matlab/ref/trapz.html>

[Rizwana]

Iam thankfull and greatfull for your generous help. Thank you once again :)

Answer 2

[ES]

doesn't trapz(A) solve your case?

[Rizwana]

f(x) or A is some data. Not a function

[ES]

I think I understand your question. trapz is a numerical integration method to which you supply a set of discontinued numbers. trapz will form trapezoids by interpolation, find the area under the curve. Look here

Answer 3

[Simon]

Hi!

Trapeziod rule means you add both values on the right and left of your discretisation, multiply with the distance and take half of it. The integral is the sum over all such areas:

Integral = sum(((A1(1:end-1) + A1(2:end)) * 0.1) / 2);

[Rizwana]

Hi. Can you please elaborate your explaination little more.

[Simon]

You can write it as a loop like

% start at 0
Integral = 0;

% loop over all values (except the last one)
for n = 1:length(A1)-1
  % values on both sides
  leftvalue = A1(n);
  rightvalue = A1(n+1);
  % trapezoid area (0.1 is your t1 discretisation)
  area = ((leftvalue+rightvalue) * 0.1) / 2;
  % sum up whole area
  Integral = Integral + area;
end

I think in your question you mix the "index" into the A1 array and the "position" in t1. If you need a position in t1, lets say 1.3, you can do

ind = find(t1 == 1.3);

This is the index in t1 and the index in A1, so the value at t=1.3 is in

ind = find(t1 == 1.3);
A1(ind)

[Rizwana]

Thank You.