Plot cross sections of a function

Question

I have been learning how to use Mathematica for the past few weeks, and recently I have been trying to recreate something along the lines of this.

Given a function, I want to create a 3d plot of an object as if the bounded regions of the function were to be extruded upwards in a certain shape. From this I hope to find a basic volume, instead of integrating. How would I do this? I have seen ParametricPlot3D, but I haven't been able to create what I want with it.

Answer 1

ParametricPlot3D[{v {u, Sin[u], 0} + (1 - v) {u, -Sin[u], 0},
  ConditionalExpression[v {u, Sin[u], 0} + (1 - v) {u, 0, Sin[u]},  0 <= u <= Pi],
  ConditionalExpression[v {u, -Sin[u], 0} + (1 - v) {u, 0, Sin[u]}, 0 <= u <= Pi],
  {u, 0, Sin[u]}},
  {u, -1, 4}, {v, 0, 1},
  PlotStyle -> Opacity[.5, White], Lighting -> "Neutral",
  Boxed -> False, Axes -> True, BoxRatios -> {2, 1, 1},
  MeshFunctions -> {Function[{x, y, z, u, v}, u], Function[{x, y, z, u, v}, v]},
  Mesh -> {Range[0, Pi, Pi/4], {0, 1}},
  MeshStyle -> {Directive[Dashed, Red], Directive[Thick, Blue]},
  PlotRange -> Full, ImageSize -> 500, AxesOrigin -> {0, 0, 0},
  Ticks -> {{Pi/2, Pi}, {-1/2, -1}, {1/2, 1}},
  PlotRangePadding -> .2,  AxesStyle -> Thick, ImageSize -> 500]

Update: a first attempt to use RegionPlot3D:

RegionPlot3D[-Abs@Sin[x] <= Abs@y <= Abs@Sin[x] && z + Abs@y <= Abs@Sin[x] && 0 <= z,
 {x, 0, Pi}, {y, -1, 1}, {z, -1, 1},
 PlotRange -> {{-1, Pi + 1/2}, {-1, 1}, {-1, 1}},
 BoxRatios -> {2, 1, 1},
 PlotStyle -> Directive[White, Opacity[0.6]], Lighting -> "Neutral",
 PlotPoints -> 35,
 MeshFunctions -> {#1 &, #2 &, #3 &},
 Mesh -> {{.5, 1., 1.5, 2., 2.1, 2.2, 2.3}, {0.}, {0.}},
 MeshStyle -> {Directive[Thin, Gray], Directive[Thick, Blue], Directive[Thick, Blue]},
 Axes -> True, AxesStyle -> Thick,
 AxesOrigin -> {0, 0, 0}, Ticks -> {{Pi/2, Pi}, {-1/2, -1}, {1/2, 1}},
 ImageSize -> 500, Boxed -> False]