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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