【摘要】 解决计算旋转曲面面积尚无具有普遍适用性的统一公式之问题.依据古鲁金第一定理推证,得到利用曲线积分计算空间某一平面上的曲线Γ绕直线(轴)L旋转而成的旋转曲面面积的通用公式;利用曲线积分计算xoy面上的曲线c绕直线(轴)L旋转而成的旋转曲面面积的通用公式.依据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曲面面积的具有针对性的公式.更多还原

【Abstract】 The problem that there is no general formula on calculating the rotating surface area is solved.Based on the Guldin′s first theorem,it was deduced that the general formula to calculate the rotating surface area which is shaped by rotating the curve Γ in a plane around the L-axis in the space by using curve integral.The general formula to calculate the rotating surface area which is shaped by rotating the curve c in xoy plane around the L-axis by using curve integral.According to the general formulas derived by this paper,the targeted formula to calculat the rotating surface area by using definite integral in specific cases is deduced.更多还原