惯性矩计算器
逐步求区域/面积的面积二次矩和回转半径
该计算器将尝试求出由给定曲线围成的区域（面积）的惯性矩和回转半径，并显示计算步骤。
您的输入
求由曲线$$$y = 3 x$$$, $$$y = x^{2}$$$围成的区域的惯性矩。
解答
$$$I_{x} = \int\limits_{0}^{3}\int\limits_{x^{2}}^{3 x} y^{2}\cdot 1\, dy\, dx = \frac{2187}{28}\approx 78.107142857142857$$$
$$$I_{y} = \int\limits_{0}^{3}\int\limits_{x^{2}}^{3 x} x^{2}\cdot 1\, dy\, dx = \frac{243}{20} = 12.15$$$
$$$m = \int\limits_{0}^{3}\int\limits_{x^{2}}^{3 x} 1\, dy\, dx = \frac{9}{2} = 4.5$$$
$$$R_{x} = \sqrt{\frac{I_{x}}{m}} = \frac{9 \sqrt{42}}{14}\approx 4.166190448976482$$$
$$$R_{y} = \sqrt{\frac{I_{y}}{m}} = \frac{3 \sqrt{30}}{10}\approx 1.643167672515498$$$
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