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| 极坐标系下旋转体体积公式的推广 | |
| 引用本文： | 陈珍培. 极坐标系下旋转体体积公式的推广[J]. 大学数学, 2014, 0(1): 96-100 |
| 作者姓名： | 陈珍培 |
| 作者单位： | 浙江树人大学基础部,浙江杭州310015 |
| 摘 要： | 利用微积分的有关知识,对极坐标系下旋转体的体积公式进行了推广,推导并证明了极坐标系下曲边扇形绕任意空间直线(过极点)旋转所得旋转体的体积计算公式,证明了有关性质,并借助实例进行说明. |
| 关 键 词： | 旋转体 极坐标 曲边扇形 定积分 三重积分 |
The Generalization of the Formula about Volume of the Solid of Revolution in Polar Coordinate System |
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| CHEN Zhen-pei. The Generalization of the Formula about Volume of the Solid of Revolution in Polar Coordinate System[J]. College Mathematics, 2014, 0(1): 96-100 | |
| Authors: | CHEN Zhen-pei |
| Affiliation: | CHEN Zhen-pei (Basic Courses Dept of Zhejiang Shuren University, Hangzhou,Zhejiang 310015,China) |
| Abstract: | Based on the knowledge of definite integration, the formula about volume of the solid of revolution in polar coordinate system be generalized, A formula about the volume of the solid of revolution generated by a curvilinear sector, in polar coordinate, around any straight line in space be obtained. Two properties are proofed, and two examples are provided to demonstrate the application of the formula. |
| Keywords: | revolution solid~ polar coordinate system~ curvilinear sector~ definite integrals~ triple integrals |
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