One of the most important applications of integrals is to calculate the arc length of a curve in plane.The calculation and proof indicated that the formula of the element of arc length in polar coordinates can only be ds=ρ θ ρ θ θ′+ ,not be d 2 ( ) ( )2 ( ) ds=ρ(θ)dθ .% 平面曲线弧长的计算是定积分在几何上一个非常重要的应用。通过计算与证明相结合，说明弧长元素的极坐标公式只能为s ρθρθθ′=d 2()+()2() d ，而不能为ds=ρ(θ)dθ
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