我有以下图表，我想用它们来说明计算通过旋转函数得到的旋转体的体积
y=2e^{-(1/2)x}
从 a 到 b，通过圆盘（绕 x 轴旋转）和壳（绕 y 轴旋转）。我尝试改编一些帖子，但都没有成功。
简要描述一下我想要做的事情：i）制作一个直径为 2f（x）（从 y=-f（x）到 y=f（x））的距离（像一枚硬币立在边缘）；ii）围绕 y 轴制作一个壳或垫圈。
如果有人有我可以适应我的目的（针对上述任一或两者）的代码，我将不胜感激。
由于我似乎无法附加该图，下面是我用来生成第一个图的代码。由于空间限制（30000 个字符，我无法包含第二个图的代码。但它与第一个类似，只是围绕 y 轴旋转）。
第一个图
\documentclass[12pt,tikz]{standalone}
\usepackage{tikz-3dplot}
\usetikzlibrary{shapes.geometric, decorations.pathreplacing, matrix, angles, quotes, arrows, arrows.meta, datavisualization,cd}
\usetikzlibrary{through,calc,intersections}
\usepackage{mathrsfs}
\usetikzlibrary{arrows}
\begin{document}
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(1.2,-0.1) -- node[below=2.5pt] {\footnotesize $\Delta x$} (1.4,-0.1);
\draw (2.5,0.8) node[anchor=center,rotate=-22] {\footnotesize $y=fx)$};
\draw (0.5,-0.1) node[anchor=center,rotate=-22] {\footnotesize $a$};
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\end{document}
答案1
运行xelatex
\documentclass{article}
\usepackage{pst-func}
\begin{document}
\psset{algebraic}
\noindent
\begin{pspicture}(-0.5,-2.5)(5,2.5)
\psaxes{->}(0,0)(0,-2)(3,2.5)
\psVolume[fillstyle=solid,fillcolor=magenta!30](0,4){1}{sqrt(x)}
\psline{->}(4,0)(5,0)
\end{pspicture}
%
\begin{pspicture}(-0.5,-2.5)(5,2.5)
\psaxes{->}(0,0)(0,-2)(3,2.5)
\psVolume[fillstyle=solid,fillcolor=red!40](0,4){2}{sqrt(x)}
\psline{->}(4,0)(5,0)
\end{pspicture}
%
\begin{pspicture}(-0.5,-2.5)(5,2.5)
\psaxes{->}(0,0)(0,-2)(3,2.5)
\psVolume[fillstyle=solid,fillcolor=blue!40](0,4){4}{sqrt(x)}
\psline{->}(4,0)(5,0)
\end{pspicture}
\begin{pspicture}(-0.5,-2.5)(5,2.5)
\psaxes{->}(0,0)(0,-2)(3,2.5)
\psVolume[fillstyle=solid,fillcolor=green!40](0,4){8}{sqrt(x)}
\psline{->}(4,0)(5,0)
\end{pspicture}
%
\begin{pspicture}(-0.5,-2.5)(5,2.5)
\psaxes{->}(0,0)(0,-2)(3,2.5)
\psVolume[fillstyle=solid,fillcolor=yellow!40](0,4){16}{sqrt(x)}
\psline{->}(4,0)(5,0)
\end{pspicture}
%
\begin{pspicture}(-0.5,-2.5)(5,2.5)
\psaxes{->}(0,0)(0,-2)(3,2.5)
\psVolume[fillstyle=solid,fillcolor=cyan!40](0,4){32}{sqrt(x)}
\psline{->}(4,0)(5,0)
\end{pspicture}
\end{document}
或者使用你的功能：
\def\func{2*Euler^(-1/2*x)}
和
\begin{pspicture}(-0.5,-2.5)(5,2.5)
\psaxes{->}(0,0)(0,-2)(3,2.5)
\psVolume[fillstyle=solid,fillcolor=magenta!30](0,4){1}{\func}
\psline{->}(4,0)(5,0)
\end{pspicture}
