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我怎样才能给这条地带涂上油漆？

tag-icon • tag-icon tikz-pgf
我怎样才能给这条地带涂上油漆？

我需要给条带上色。函数是 $y = \frac{1}{x}$ 我可以画图，但不能给条带上色\;\

\begin{center}
\begin{tikzpicture}
    \draw[->] (-1,0) -- (7,0) node[right] {$x$};
   \draw[->] (0,-1) -- (0,4) node[above] {$y$};
   \draw[scale=1.5,domain=0.35:4,smooth, variable=\x,black, ultra thick] plot ({\x},{1/(\x)});
\draw[dashed] (3,0)--(3,0.75);
\draw[dashed] (0,0.75)--(3,0.75);
    \node at (-0.5,0.75){$\frac{1}{b}$};
    \node at (3,-0.3){$b$};
        \node at (1,-0.3){$a$};
  \node at (-0.5,2.2) {$\frac{1}{a}$};
\draw[dashed] (1,0)--(1,2.2);
\draw[dashed] (0,2.2)--(1,2.2);
\node at (1,2.2) {$\bullet$};
    \node at (3,0.75) {$\bullet$};
\end{tikzpicture}
\end{center}

在此处输入图片描述

答案1

带有软件包的解决方案mfpic，适用于可能感兴趣的 MetaPost（和 METAFONT）的 LaTeX 界面。

填充是通过以下指令实现的

\gfill[.5(red+white)]\btwnfcn{1, 3, .1}{0}{f(x)}

\btwnfcn0产生由两个函数（这里和f(x)）和垂直线（这里是方程x=1和）形成的闭合路径x=3，然后对其进行填充。

请注意，由于 OP 示例中的函数路径按 1.5 倍缩放，因此我倾向于将其定义f(x)为等于2.25/x而不是1/x。它产生的路径与缩放相同，并且以这种方式处理它要容易得多。

\documentclass[border=2mm]{standalone}
\usepackage[metapost, mplabels, truebbox]{mfpic}
  \mfpverbtex{%&latex
    \documentclass{article}
    \usepackage{amsmath}
    \begin{document}}
  \setlength{\mfpicunit}{1cm}
  \opengraphsfile{\jobname}
\begin{document}
  \begin{mfpic}[1]{-1}{7}{-1}{5}
    \fdef{f}{x}{2.25/x}
    \gfill[.5(red+white)]\btwnfcn{1, 3, .1}{0}{f(x)}
    \dashed\lines{(1, 0), (1, f(1)), (0, f(1))}
    \dashed\lines{(3, 0), (3, f(3)), (0, f(3))}
    \doaxes{xy}
    \penwd{1.2bp}
    \function{.5, 6, .1}{f(x)}
    \tlpointsep{3bp}
    \tlabels{[tr]{origin}{$O$} [tc]{(\xmax, 0)}{$x$} [cr]{(0, \ymax)}{$y$}
      [tc]{(1, 0)}{$a$} [tc]{(3, 0)}{$b$} 
      [cr]{(0, f(1))}{$\dfrac{1}{a}$} [cr]{(0, f(3))}{$\dfrac{1}{b}$}}
  \end{mfpic}
  \closegraphsfile
\end{document}

先运行 (PDF)LaTeX，然后运行 ​​MetaPost，最后再次运行 (PDF)LaTeX。输出：

在此处输入图片描述

答案2

只需在曲线下方填充即可。

\documentclass[10pt,letterpaper]{article}
\usepackage{tikz}
\begin{document}

\begin{center}
\begin{tikzpicture}
\fill [red!50, domain=1:3, variable=\x]
  (1, 0)
  -- plot ({\x}, {2.2/(\x)})
  -- (3, 0)
  -- cycle;      \draw[->] (-1,0) -- (7,0) node[right] {$x$};
   \draw[->] (0,-1) -- (0,4) node[above] {$y$};
   \draw[scale=1.5,domain=0.35:4,smooth, variable=\x,black, ultra thick] plot ({\x},{1/(\x)});
\draw[dashed] (3,0)--(3,0.75);
\draw[dashed] (0,0.75)--(3,0.75);
    \node at (-0.5,0.75){$\frac{1}{b}$};
    \node at (3,-0.3){$b$};
        \node at (1,-0.3){$a$};
  \node at (-0.5,2.2) {$\frac{1}{a}$};
\draw[dashed] (1,0)--(1,2.2);
\draw[dashed] (0,2.2)--(1,2.2);
\node at (1,2.2) {$\bullet$};
    \node at (3,0.75) {$\bullet$};
\end{tikzpicture}
\end{center}

\end{document}

在此处输入图片描述

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