MATLAB: Calculate area between unknown curve and straight line

Question

How can I calculate areas between these unknown curve and line, see image. The line is not zero.

How can I use trapz in this case? it would calculate the area under the curve from zero line

Areas under the line should be negative

theta=0:10:710;
T=[0 15 813 964 1016 936 775 642 695 850 1032 1029 904 712 608 592 545 344 0 -346 -540 -578 -569 -636 -784 -877 -815 -570 -325 -191 -203 -237 -165 5 149 146 0 -143 -149 -7 164 236 201 191 324 570 815 879 786 640 569 574 538 344 0 -343 -541 -578 -574 -645 -792 -893 -836 -606 -380 -264 -298 -369 -332 -197 -56 2];
W=trapz(theta,T);
T_avg=W/710;
plot(theta,T)
hold on
plot(theta,T_avg*ones(size(theta)))

Answer 1

The areas below the line are negative:

AboveLine = T>=T_avg;                                           % Logical Vector
AreaAboveLine = trapz(theta(AboveLine), T(AboveLine))
AreaBelowLine = trapz(theta(~AboveLine), T(~AboveLine))
AreaTotal = AreaAboveLine + AreaBelowLine

producing:

AreaAboveLine =
      235685
AreaBelowLine =
     -147420
AreaTotal =
       88265

EDIT —

Try this:

theta=0:10:710;
T=[0 15 813 964 1016 936 775 642 695 850 1032 1029 904 712 608 592 545 344 0 -346 -540 -578 -569 -636 -784 -877 -815 -570 -325 -191 -203 -237 -165 5 149 146 0 -143 -149 -7 164 236 201 191 324 570 815 879 786 640 569 574 538 344 0 -343 -541 -578 -574 -645 -792 -893 -836 -606 -380 -264 -298 -369 -332 -197 -56 2];
W=trapz(theta,T);
T_avg=W/710;
plot(theta,T)
hold on
plot(theta,T_avg*ones(size(theta)))
hold off
zci = @(v) find(v(:).*circshift(v(:), [-1 0]) <= 0);                    % Returns Approximate Zero-Crossing Indices Of Argument Vector
Tzx = zci(T - T_avg);                                                   % Zero-Crossing Indices
Tidx = [1; Tzx; numel(T)];                                              % All Relevant Indices
for k = 1:numel(Tidx)-1
    idxrng = Tidx(k):Tidx(k+1);
    Areas(k) = trapz(theta(idxrng), T(idxrng)-T_avg);
    ctrs(k,:) = [mean(theta(idxrng)) mean(T(idxrng))];
end
for k = 1:size(ctrs,1)
    text(ctrs(k,1),ctrs(k,2), sprintf('%.0f', Areas(k)), 'HorizontalAlignment','left', 'VerticalAlignment','middle'
end

Make appropriate changes to get the result you want.