摘要
为解决计算旋转体体积尚无具有普遍适用性的统一公式的问题,依据古鲁金第二定理推证得到:利用曲面积分计算空间某一平面图形Σ绕直线(轴)L旋转而成的旋转体体积的通用公式;利用二重积分计算xoy面上的平面图形D绕直线(轴)L旋转而成的旋转体体积的通用公式。依据本文所证得的通用计算公式推证得到:在某些特定情形下利用定积分计算旋转体体积的具有针对性的公式。
In order to solve the problem of calculating rotating body volume without the general unified formula, based on Guldin＇ s second theorem, the general formulas are deduced on calculating the volume of the rotating body shaped by rotating the plane figure Σ around the L-axis in the space by using surface integral and calculating the volume of the rotating body shaped by rotating the plane figure D in xoy plane around the L-axis by using double integral. According to these general formulas, the targeted formula to calculate the rotating body volume by using definite integral in some specific cases is derived in this paper.
出处
《西安理工大学学报》
CAS
2008年第3期362-365,共4页
Journal of Xi'an University of Technology
关键词
直线
平面图形
旋转体
旋转体体积
straight line
plane figure
rotating body
rotating body volume
