Fourier series doesnt overlap function

b = zeros(1,7);
x = linspace(-2,2,200);
f = ((8+x.^3)).^(1/2);

b0 = trapz(x,f);

for n = 1:7
    y = f.*sin(n*pi*x/2);
    b(n) = trapz(x,y);
end

fh = zeros(1,200);

for n = 1:7
    fh = fh + b(n)*sin(n*pi*x/2);
end

fh = b0/2 + fh;

plot(x,f,'r','LineWidth',3)
hold on
plot(x,fh,'b','LineWidth',1)
hold off
legend('f','fh','Location','best')
title('N/A')

Can anyone see why the fourier series of f doesnt line up with the function f?