具体到心形线\(r=a(1+\cos\theta)\)，首先需要求出\(r\)对\(\theta\)的导数。导数\(r' = -a\sin\theta\)。将\(r\)和\(r'\)代入弧长公式，得到：\(\int_{0}^{\pi} \sqrt{[a(1+\cos\theta)]^2 + (-a\sin\theta)^2} d\theta\)。化简得：\(\int_{0}^{\pi} \sq...
极坐标:\displaystyle \rho=a(1+cos\theta), \theta\in[0,2\pi],a>0 直角坐标:\displaystyle x^2+y^2-ax=a\sqrt{x^2+y^2},a>0 参数方程:\displaystyle\left\{ \begin{array}{lc} x=a(1+cos\theta)cos\theta\\ y=a(1+cos\theta)sin\theta\\ \end{array} \right.(a>0,\theta\in[0...