Having trouble with integral and matrix range.

I need to calculate the integral fo Fo value (wich is used in food industry for determining if sterilization or pasteurization was complete).

Fo = INT(10^((T(t)-Tr)/z)*dt),0,time)

in which:

Tr,z = constants

T = matrix, in this form:

16 17 18 19 20.....

time = matrix, just like T matrix:

5 6 7 8....

How can i accomplish this integral? I have to calculate it numerically with this values, but i don't find how :(

Also, within my programming i get a matrix which is always ONE cell longer than all the other arrays (matlab always goes +1 for the calculation, so i get a longer array). I need to program that this doesn't happen, so i can plot this matrices (which now i can't, because of the different ranges of the arrays. i have to erase the last cell manually)

Help please :(

Best regards

Answer 1

[Walter Roberson]

Your derivative indicator, dt, is only meaningful if t is continuous. If your T(t) term indicates indexing, then your t needs to be discrete positive integers.

If you were to modify the expression to

Fo = integral of 10^((T*t-Tr)/z)*dt over t = 0 to time

[since a(b) might mean a*(b) which would normally be written a*b unless b is an expression] then you have two difficulties: that T is a vector, and that time is a vector.

Perhaps you want to define,

Fo(k) = integral of 10^((T(k)-Tr)/z)*dt over t = 0 to time(k)

where in that line (k) indicates indexing at offset k.

If that is what you want, then the answer becomes trivial:

Fo(k) = 10^((T(k)-Tr)/z) * time(k)

since in that circumstance 10^((T(k)-Tr)/z) would simply be a constant for the purposes of integration.

For the second part of your question about an output that is too long, we would need to see code.

[Walter Manns]

What i'm asking in the second part, is just this:

How can i, with a command/function, transform this matrix:

A = [1 2 3 4 5]

to this one:

A' = [1 2 3 4]

Just erase the last cell.

Regards :D

[Walter Roberson]

A(1:end-1)

However, it would be better to construct the code so that the extra value was not generated, if possible. (It isn't always possible, but it is more often than not.)