function A = coef(alpha)
   % Do not change the function name, number of input and output variables.
   % In this function you have to calculate the coef. A0 to A20 using integrations.
   % The input is only the angle of attack in radian, and the output is a vector array
   % with 21 elements. The first element is A0, and the last element is A20.
   % Note that this function and dcamber do not need the chord length.
   A = zeros(21,1);
   i = 0;
   angle = acos(1-2*0.2025);
   A(1) = alpha - (1/pi)*(integral(@(theta) dcamber(theta).*cos(i*theta),0,angle) + integral(@(theta) dcamber(theta).*cos(i*theta),angle,pi));
   for i = 1:20
      A(i+1) = (2/pi) * (integral(@(theta) dcamber(theta).*cos(i*theta),0,angle) + integral(@(theta) dcamber(theta).*cos(i*theta),angle,pi));
   end
   % Write a loop that goes over the calculation of each element of A using the dz/dx
   % defined in dcamber function.
   % Remember that some functions are defined using the auxiliary variable theta, and
   % some are based on x/c and z/c.
   % Use any integration method you like. But, you may need to increase the accuracy
   % to be able to generate the same coef. as the reference code.
end

function dzdx = dcamber(theta)
   % write a function that calculates dz/dx for each value of theta. You may want to
   % create a function that works with a vector array as theta and generates a vector
   % array dzdx corresponding to each element of input.
   xc = 0.5*(1-cos(theta));
   if xc <= 0.2025
       dzdx = 2.6595*(3*(xc).^2 - 1.2150*xc + 0.1147);
   else
       dzdx = -0.02208;
   end
end