diff --git a/advanced-math/exercise/4-integal-of-functions-of-single-variable/integal-of-functions-of-single-variable.pdf b/advanced-math/exercise/4-integal-of-functions-of-single-variable/integal-of-functions-of-single-variable.pdf
index 0866b2a..2f06f1d 100644
Binary files a/advanced-math/exercise/4-integal-of-functions-of-single-variable/integal-of-functions-of-single-variable.pdf and b/advanced-math/exercise/4-integal-of-functions-of-single-variable/integal-of-functions-of-single-variable.pdf differ
diff --git a/advanced-math/exercise/4-integal-of-functions-of-single-variable/integal-of-functions-of-single-variable.tex b/advanced-math/exercise/4-integal-of-functions-of-single-variable/integal-of-functions-of-single-variable.tex
index 9de089c..d7fd111 100644
--- a/advanced-math/exercise/4-integal-of-functions-of-single-variable/integal-of-functions-of-single-variable.tex
+++ b/advanced-math/exercise/4-integal-of-functions-of-single-variable/integal-of-functions-of-single-variable.tex
@@ -1054,7 +1054,7 @@ $\therefore I_n=n!$。
     \item 若只存在$\rho=1$，使得$\lim\limits_{x\to+\infty}xf(x)=c>0$或为$-\infty$，则积分发散。
 \end{itemize}
 
-\subsubsection*{无界函数}
+\subsubsection{无界函数}
 
 对于瑕积分$\int_a^bf(x)\,\textrm{d}x$，其中$a$为瑕点，$f(x)$在$[a,b]$上连续非负，对于常数$\rho$：
 
diff --git a/advanced-math/knowledge/4-indefinite-integral-and-definite-integral/indefinite-integral-and-definite-integral.pdf b/advanced-math/knowledge/4-indefinite-integral-and-definite-integral/indefinite-integral-and-definite-integral.pdf
index 554712c..fdce19b 100644
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diff --git a/advanced-math/knowledge/4-indefinite-integral-and-definite-integral/indefinite-integral-and-definite-integral.tex b/advanced-math/knowledge/4-indefinite-integral-and-definite-integral/indefinite-integral-and-definite-integral.tex
index 2b6cd38..d3ab450 100644
--- a/advanced-math/knowledge/4-indefinite-integral-and-definite-integral/indefinite-integral-and-definite-integral.tex
+++ b/advanced-math/knowledge/4-indefinite-integral-and-definite-integral/indefinite-integral-and-definite-integral.tex
@@ -773,6 +773,10 @@ $\overline{x}=\dfrac{\int_\alpha^\beta x(t)\sqrt{x'^2(t)+y'^2(t)}\textrm{d}t}{\i
 
 $\overline{y}=\dfrac{\int_\alpha^\beta y(t)\sqrt{x'^2(t)+y'^2(t)}\textrm{d}t}{\int_\alpha^\beta\sqrt{x'^2(t)+y'^2(t)}\textrm{d}t}$。
 
+设质量分布不均的光滑物体曲线$\overset{\frown}{AB}$，区间为$[\alpha,\beta]$，线密度为$\rho(x)$。
+
+$\overline{x}=\dfrac{\int_\alpha^\beta x\rho(x)\,\textrm{d}x}{\int_\alpha^\beta\rho(x)\,\textrm{d}x}$。
+
 \paragraph{平面} \leavevmode \medskip
 
 设曲边梯形平面区域$D=\{(x,y)|0\leqslant y\leqslant f(x),a\leqslant x\leqslant b\}$，$f(x)$在$[a,b]$上连续，则平面$D$的形心坐标计算公式为：\medskip