问题
如下图所示,如何用定积分表示由函数 $\Omega(x)$ 和 $\Delta(x)$ 以及直线 $y$ $=$ $a$ 和 $y$ $=$ $b$ 所围成的平面图形的面积 $S$?选项
[A]. $S$ $=$ $\int_{c}^{d}$ $| \Omega(x) – \Delta(x) |$ $\mathrm{d} x$[B]. $S$ $=$ $\int_{c}^{d}$ $[\Omega(x) + \Delta(x)]$ $\mathrm{d} x$
[C]. $S$ $=$ $\int_{c}^{d}$ $| \Omega(x) + \Delta(x) |$ $\mathrm{d} x$
[D]. $S$ $=$ $\int_{c}^{d}$ $[\Omega(x) – \Delta(x)]$ $\mathrm{d} x$
$S$ $=$ $\int_{\textcolor{Orange}{c}}^{\textcolor{Orange}{d}}$ $\textcolor{Yellow}{|} \textcolor{Red}{\Omega(x)} – \textcolor{cyan}{\Delta(x)} \textcolor{Yellow}{|}$ $\mathrm{d} x$
或者写成:
$S$ $=$ $\int_{\textcolor{Orange}{c}}^{\textcolor{Orange}{d}}$ $\textcolor{Yellow}{|} \textcolor{cyan}{\Delta(x)} – \textcolor{Red}{\Omega(x)} \textcolor{Yellow}{|}$ $\mathrm{d} x$