example13.1.tex

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% ----------------------------------------------------------------------------------------
%	TITLE
% ----------------------------------------------------------------------------------------
\begin{document}
\begin{CJK}{UTF8}{gkai}
  \title{\textbf{例13.1}}
  % \setlength\epigraphwidth{0.7\linewidth}
  \author{\small{叶卢庆}\\{\small{杭州师范大学理学院,学
        号:1002011005}}\\{\small{Email:h5411167@gmail.com}}} % Institution
  \renewcommand{\today}{\number\year. \number\month. \number\day}
  \date{\today} % Date
  
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  \maketitle % Print the title section
  
  % ----------------------------------------------------------------------------------------
  %	ABSTRACT AND KEYWORDS
  % ----------------------------------------------------------------------------------------
  
  % \renewcommand{\abstractname}{摘要} % Uncomment to change the name of the abstract to something else
  
  % \begin{abstract}
  
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  % \hspace*{3,6mm}\textit{关键词:} % Keywords
  
  % \vspace{30pt} % Some vertical space between the abstract and first section
  
  % ----------------------------------------------------------------------------------------
  %	ESSAY BODY
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  \begin{example}[13.1]
    求 $f(x,y,z)=x-3y^2+z$ 在原点与点 $(1,1,1)$ 连线段 $C$ 上的积分.
  \end{example}
  \begin{proof}[解]
曲线 $l$ 的方程为
$$
\begin{cases}
  x(t)=t,\\
y(t)=t,\\
z(t)=t.\\
\end{cases}
$$
其中 $0\leq t\leq 1$.因此可得积分
$$
\int_0^1 (-3t^2+2t)\sqrt{3}dt=0.
$$
\end{proof}
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  %	BIBLIOGRAPHY
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\end{document}