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Routines inside Epilog

I need to plot many lines between a curve and the x-axis for to show an
 approximation of the area under the curve. 
f[x_] := 36 - 4*(x - 3)^2

Plot[f[x], {x, 0, 3}]

Plot[f[x], {x, 0, 3}, Epilog -> {Line[{ {0.2, 0}, {0.2, f[0.2]}, {0.4, 
f[0.2]} }], Line[{ {0.4, 0},{0.4, f[0.4]},{0.6, f[0.4]}}]]

All the above-mentioned works correctly. However, I am not able to 
create a routine for several similar lines, as:

 Plot[f[x], {x, 0, 3}, Epilog -> Do[Line[{ {i, 0}, {i, f[i]}, {i+.2, 
f[i]} }],{i,15} ]]

Where is my error?   
Thank you very much.


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