Numerical integration of area

Hi,

I know this must be so easy but I'm confused. I have a section such as this:

I have both variables depth and distance as vectors:

>> whos depth rotx
  Name        Size            Bytes  Class     Attributes

  depth      69x1               552  double              
  rotx       69x1               552  double              

What is the right way to compute the section area?

Thanks!

Answer 1

[John D'Errico]

The region in color? The integral will be negative, or course, since depth is entirely negative.

But you perform such an integration using trapz. The integration you need to do is the difference between the lower limit at any x, and the upper limit, which is 0. As such,

trapz(depth,0-rotx) % Not this, of course.

Read the help for trapz.

Edit: (Duh) Repairing my sleepy code:

trapz(rotx,0-depth)

[user20912]

Do you mean to use the X variable (rotx) as the first or second argument in the trapz function?

Should not be ?

trapz(rotx,0-depth)

[John D'Errico]

Of course, I did. Is that not what I wrote? ;-)

I admit, I always forget, since trapz tries to be tricky. You can call it with 1 or 2 arguments. With 2 arguments, you call it as trapz(x,y), but with only one argument, it is just trapz(y). Personally, I never liked the way they did it.

help trapz

 TRAPZ  Trapezoidal numerical integration.
    Z = TRAPZ(Y) computes an approximation of the integral of Y via
    the trapezoidal method (with unit spacing).  To compute the integral
    for spacing different from one, multiply Z by the spacing increment.
 
    For vectors, TRAPZ(Y) is the integral of Y. For matrices, TRAPZ(Y)
    is a row vector with the integral over each column. For N-D
    arrays, TRAPZ(Y) works across the first non-singleton dimension.
 
    Z = TRAPZ(X,Y) computes the integral of Y with respect to X using the
    trapezoidal method. X can be a scalar or a vector with the same length
    as the first non-singleton dimension in Y. TRAPZ operates along this
    dimension. If X is scalar, then TRAPZ(X,Y) is equivalent to X*TRAPZ(Y).
 
    Z = TRAPZ(X,Y,DIM) or TRAPZ(Y,DIM) integrates across dimension DIM
    of Y. The length of X must be the same as size(Y,DIM)).
 
    Example:
        Y = [0 1 2; 3 4 5]
        trapz(Y,1)
        trapz(Y,2)
 
    Class support for inputs X, Y:
       float: double, single
 
    See also SUM, CUMSUM, CUMTRAPZ, INTEGRAL.

    Documentation for trapz
       doc trapz

    Other uses of trapz

       codistributed/trapz    gpuArray/trapz

So, yes. I meant to write

trapz(rotx,0-depth)

And apparently, my fingers got in the way of my head.

[user20912]

I feel it is easy but confuses me every time. Thanks for you help :)