Area under curve (no function)

Hello,

If I have a set of data such as

X = [0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.85];
rA = [-.0053, -.0052, -.0050, -.0045, -.0040, -.0033, -.0025, -.0018, -.00125, -.0010];
plot(X,-1./rA)

and I want to know the area under the curve generated in the graph, how would I do that? There is no function involved here, this is just raw data, so I know I can't use quad or any of those integral functions.

Thanks

[Ashok]

% Find the number of pixels of the connected component

Bin_image - logical binary image CC = bwconncomp(Bin_image); CC numPixels = cellfun(@numel,CC.PixelIdxList); disp(numPixels);

% Find the number of pixels of the connected component

[Label,~]=bwlabel((Bin_image),8); [Label,~]=bwlabel(Bin_log_4mult,8); num=1; [row, ~] = find(Label==num); Obj_area=numel(row); display(Obj_area);

[Samarth Patil]

how to find the area in an interval for such a plot?

[Krishnendu Mukherjee]

Thanks a lot. It helped a lot.

Answer 1

[Star Strider]

Use trapz. It’s designed to do exactly what you want.

Int = trapz(X, -1./rA)

produces:

Int =

     306.7455

[Rick]

now how do I know if I should do trapz(X,-1./rA) or trapz(-1./rA,X)?? Which would give the area under the curve for the plot(X,-1./rA)??

The documentation is quite unclear to me, it says

 Z = trapz(X,Y) computes the integral of Y with respect to X using
    the trapezoidal method.  X and Y must be vectors of the same
    length, or X must be a column vector and Y an array whose first
    non-singleton dimension is length(X).  trapz operates along this
    dimension.

if X is my x-axis and -1./rA is my y-axis, does that mean I should do trapz(X,-1./rA)??

[Star Strider]

‘if X is my x-axis and -1./rA is my y-axis, does that mean I should do trapz(X,-1./rA)??’

Yes. Actually, X is your independent variable and (-1./rA) is your dependent variable.

Use:

Int = trapz(X, -1./rA)

to produce:

Int =

     306.7455

[Krishnendu Mukherjee]

Thanks a lot :)

[Saurabh Parmar]

Thank You So Much! That helped a lot.

[Star Strider]

Everyone — My pleasure!

Answer 2

[Ashok]

% Find the number of pixels of the connected component

Bin_image - logical binary image CC = bwconncomp(Bin_image); CC numPixels = cellfun(@numel,CC.PixelIdxList); disp(numPixels);

% Find the number of pixels of the connected component

[Label,~]=bwlabel((Bin_image),8); [Label,~]=bwlabel(Bin_log_4mult,8); num=1; [row, ~] = find(Label==num); Obj_area=numel(row); display(Obj_area);