旋转曲面表面积计算曲线绕轴旋转时扫出的面积。
核心公式
Around x-axis: S = 2π integral y sqrt(1 + (dy/dx)2) dx
Around y-axis: S = 2π integral x sqrt(1 + (dx/dy)2) dy
Around y-axis: S = 2π integral x sqrt(1 + (dx/dy)2) dy
实用示例
Sphere check: rotating a semicircle of radius r gives S = 4πr2.
相关资源
Use Sphere, Cylinder, Cone, and cone/frustum guide.