填充函数下的区域

Question 1

可以使用相同的plot命令来构建填充区域的路径：

\fill [gray, domain=-2:2, variable=\x]
  (-2, 0)
  -- plot ({\x}, {\x*\x})
  -- (2, 0)
  -- cycle;

完整示例：

\documentclass{article}
\usepackage{tikz}

\begin{document}
  \begin{tikzpicture}
    \draw[very thin, gray!30, step=1 cm](-4.9,-3.9) grid (4.9,3.9);

    \fill [gray, domain=-2:2, variable=\x]
      (-2, 0)
      -- plot ({\x}, {\x*\x})
      -- (2, 0)
      -- cycle;

    \draw [thick] [->] (-5,0)--(5,0) node[right, below] {$x$};
     \foreach \x in {-4,...,4}
       \draw[xshift=\x cm, thick] (0pt,-1pt)--(0pt,1pt) node[below] {$\x$};

    \draw [thick] [->] (0,-4)--(0,4) node[above, left] {$y$};
     \foreach \y in {-3,...,3}
       \draw[yshift=\y cm, thick] (-1pt,0pt)--(1pt,0pt) node[left] {$\y$};

    \draw [domain=-2:2, variable=\x]
      plot ({\x}, {\x*\x}) node[right] at (1.5,2) {$f(x)=x^2$};

  \end{tikzpicture}
\end{document}

Answer

可以使用相同的plot命令来构建填充区域的路径：

\fill [gray, domain=-2:2, variable=\x]
  (-2, 0)
  -- plot ({\x}, {\x*\x})
  -- (2, 0)
  -- cycle;

完整示例：

\documentclass{article}
\usepackage{tikz}

\begin{document}
  \begin{tikzpicture}
    \draw[very thin, gray!30, step=1 cm](-4.9,-3.9) grid (4.9,3.9);

    \fill [gray, domain=-2:2, variable=\x]
      (-2, 0)
      -- plot ({\x}, {\x*\x})
      -- (2, 0)
      -- cycle;

    \draw [thick] [->] (-5,0)--(5,0) node[right, below] {$x$};
     \foreach \x in {-4,...,4}
       \draw[xshift=\x cm, thick] (0pt,-1pt)--(0pt,1pt) node[below] {$\x$};

    \draw [thick] [->] (0,-4)--(0,4) node[above, left] {$y$};
     \foreach \y in {-3,...,3}
       \draw[yshift=\y cm, thick] (-1pt,0pt)--(1pt,0pt) node[left] {$\y$};

    \draw [domain=-2:2, variable=\x]
      plot ({\x}, {\x*\x}) node[right] at (1.5,2) {$f(x)=x^2$};

  \end{tikzpicture}
\end{document}

Question 2

_{该解决方案需要软件包的最新版本pgfplots，>=1.10。}

pgfplots您还可以使用该包及其库的绘图功能fillbetween来填充两个通用曲线之间的区域。

首先，绘制要绘制的曲线并为其命名。然后，将 x 轴作为“虚构”曲线插入，该曲线实际上已绘制但未绘制，并为其命名。

最后，通过发出第三个命令来遮蔽曲线下方的区域\addplot。

\documentclass[border=5pt]{standalone}
\usepackage{pgfplots}
\usepgfplotslibrary{fillbetween}
\begin{document}
\begin{tikzpicture}
  \begin{axis}[
    axis lines=center,
    grid=major,
    ymin=-5,
    no marks,
    ]
    \addplot+[smooth,blue,name path=A] {x*x}; % actual curve
    \addplot+[draw=none,name path=B] {0};     % “fictional” curve
    \addplot+[gray] fill between[of=A and B,soft clip={domain=-4:4}]; % filling
  \end{axis}
\end{tikzpicture}
\end{document}

在此处输入图片描述

Answer