(*^

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:[font = special1; inactive; preserveAspect; ]
                                           Cylindrical Coordinates

The cell below illustrates how Mathematica  can be used to estimate a multiple integral in cylindrical coordinates.
;[s]
4:0,1;66,0;99,2;110,0;184,-1;
3:2,13,9,Times,0,12,0,0,0;1,13,9,Times,1,12,0,0,0;1,13,9,Times,2,12,0,0,0;
:[font = input; preserveAspect; ]
f[r_, theta_] := 3.0 - 2r

Est[n_] := N[Sum[Sum[
   f[j/n - 1/(2n), 2 Pi i/n - Pi/n] *
   (2 Pi/(n^2)) * (j/n - 1/(2n)),
   {i, 1, n}], {j, 1, 3n/2}]]
   
Est[10]
:[font = special1; inactive; preserveAspect; ]
The cell below illustrates how Mathematica  can evaluate iterated integrals like the ones in this module.
;[s]
3:0,0;31,1;42,0;106,-1;
2:2,13,9,Times,0,12,0,0,0;1,13,9,Times,2,12,0,0,0;
:[font = input; preserveAspect; ]
Integrate[Integrate[
  f[r, theta] * r, {theta, 0, 2 Pi}], {r, 0, 3/2}]
  
  Integrate[Integrate[
  f[r, theta] * r, {r, 0, 3/2}], {theta, 0, 2 Pi}]
^*)