There are two trapz() syntaxes that allow passing in two parameters to trapz.
The first one is obvious in the documentation and is
trapz(X, Y)
where X is a scalar or vector spacing increment for the data in Y.
The second is not obvious in the documentation but can be found once you know what to look for. It is
trapz(Y, dim)
where dim is the dimension number to operate along.
In the first iteration of your "for z" loop, z is initialized to 0. Then x=0:15/100:z is 0:15/100:0 which is the scalar 0. Scalar 0 in hand for x results in scalar y of 0. So the call trapz(x, y) is a call to trapz(0,0) .
The error message suggests that this call trapz(0,0) is being interpreted as the second syntax, trapz(Y, dim), and that trapz() then errors out when it discovers that the dim of 0 is not a valid dimension number.
You can avoid this problem by passing in three parameters to trapz(), such as
trapz(x, y, 1)
