极坐标方程与x轴围成的面积
2019-10-29 18:49:31
绕极轴的旋转，其面积 = ∫ 2πy ds = ∫ 2π rsinθ √(r^2+r'^2) dθ， where s is arc length.
推导：y = rsinθ (ds)^2 = (dx)^2 + (dy)^2 = ((-rsinθ+r'cosθ)dθ)^2 + ((rcosθ+r'sinθ)dθ)^2 = （r^2+r'^2)(dθ)^2
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绕极轴的旋转，其面积 = ∫ 2πy ds = ∫ 2π rsinθ √(r^2+r'^2) dθ， where s is arc length.
推导：y = rsinθ (ds)^2 = (dx)^2 + (dy)^2 = ((-rsinθ+r'cosθ)dθ)^2 + ((rcosθ+r'sinθ)dθ)^2 = （r^2+r'^2)(dθ)^2