3D surface plot of integrated function

I'm trying to make a 3D plot to visually represent a plot I made in 2D. I've tried using cylinder, but it creates the solid in the wrong direction, over the x or z axis instead of the y-axis. Below is my code that creates the 2D plot. Is there a way to basically create a shell around the y-axis and represent it in 3D? I've tried using mesh but I can't seem to get things set up properly. Any help would be greatly appreciated!

function value = Function
r = [1:1:350]; 
S = 0.001;
T = 2400;
t = 1;
u = ((r.^2)*S)./(4*T.*t);

syms y
Wu = zeros(size(u));
for i = 1:length(u)
    Wu(i) = integral(@(y)exp(-y)./(y),u(i),inf);
end

Q = 2400;
value = Q/(4*pi*T)*Wu;

%Plot
f1 = figure('Color', [1 1 1]);
ax1 = axes('FontSize', 18, 'FontWeight', 'bold');
plot(ax1, r, value);
title('Value v Distance');
xlabel('Distance (m)');
ylabel('Value');
set(gca,'Ydir','reverse');
ax = gca;
ax.FontSize = 13;
grid on;
end

Answer 1

[DGM]

You can use cylinder. You just need to orient it as needed. For orthogonal rotations, that's easy enough.

r = [1:1:350]; 
S = 0.001;
T = 2400;
t = 1;
u = ((r.^2)*S)./(4*T.*t);
syms y
Wu = zeros(size(u));
for i = 1:length(u)
    Wu(i) = integral(@(y)exp(-y)./(y),u(i),inf);
end
Q = 2400;
value = Q/(4*pi*T)*Wu;

clf
if true % <<-- this is just for sake of testing
	[X,Y,Z] = cylinder(value);
	h=surf(Y,Z,X)
	
    % make it fancy
	shading flat
	lightangle(-90,30)
	h.FaceLighting = 'gouraud';
	h.SpecularStrength = 0.5;
	h.AmbientStrength = 0.3;
	h.DiffuseStrength = 0.9;

else
	ax1 = axes('FontSize', 18, 'FontWeight', 'bold');
	plot(ax1, r, value);
	title('Value v Distance');
	xlabel('Distance (m)');
	ylabel('Value');
	set(gca,'Ydir','reverse');
	ax = gca;
	ax.FontSize = 13;
	grid on;
end

[Alyssa Pope]

That's it!! Thank you very much!