Error while integrating with changing value of alpha and beta

I am getting error in this code

x=-5:0.1:5;
a=5;
alpha=linspace(0,30*pi/180,12);
beta=linspace(0,30*pi/180,12);
Z=3;
for i=1:length(x)
   z(i)=sqrt(a^2-x(i).^2);
   Q1=quad(@(y)pi/180*sqrt((a^2-x(i)^2-y.^2).*( ( -Z*sin(beta).*sin(alpha) - y.*cos(alpha) ).^2+( cos(alpha)*x(i) + cos(beta)*sin(alpha) *Z) .^2)),0,z(i));
   if Q1>=pi/2
      Q1= rem(Q1,pi/2);
   elseif Q1<=-pi/2
      Q1= rem(Q1,-pi/2);
   end
   Q2(i)=abs(Q1);
end
k=0.23;
Fn=2500;wo=15;va=5;
h=-((3*k*Fn*wo)/(pi*va*a^3))*Q2
plot(x,h)
grid on
xlabel('tool Path')
ylabel('Material Removal Depth')

I am getting this error

Error in quad (line 67)
y = f(x, varargin{:});

Error in Untitled6 (line 8)
   Q1=quad(@(y)pi/180*sqrt((a^2-x(i)^2-y.^2).*( ( -Z*sin(beta).*sin(alpha) - y.*cos(alpha) ).^2+( cos(alpha)*x(i) +
   cos(beta)*sin(alpha) *Z) .^2)),0,z(i));

Answer 1

[Walter Roberson]

   Q1=quad(@(y)pi/180*sqrt((a^2-x(i)^2-y.^2).*( ( -Z*sin(beta).*sin(alpha) - y.*cos(alpha) ).^2+( cos(alpha)*x(i) + cos(beta)*sin(alpha) *Z) .^2)),0,z(i));

alpha and beta are vectors. cos(beta) * sin(alpha) is an attempt to use the * operator between two 1 x 12 arrays, but * is algebraic matrix multiplication which requires that the second dimension of the first operand be the same as the first dimension of the second operand.

quad is going to pass in a vector of y values, not a scalar. y.*sin(alpha) is going to be a size mismatch unless y happens to be a column vector, but it will be a row vector.

Each of the function calls must return a vector the same size as the input.

Please consider what you are doing further. If the quad worked with the vector of angles you would expect one result for each angle, but your code expects a single scalar output.