2\sqrt{2}\pi {a}^{2}(1+cos\theta )(3/2)d\theta把积分变量代换成θ/2,可以比较容易地解出定积分式:16πa^2*(x-x^3/3),x=sin(θ/2)总的表面积是从0到π的积分.当然,如果说心形线凹进去的部分不算侧面积,只要求出沿极轴方向离顶点最远的点的θ=2π/3,并把它做为积分上限即可.结...
即：\(\int_{0}^{\pi} a\sqrt{2(1+\cos\theta)} d\theta\)。使用三角恒等式\(\cos\theta = 1-2\sin^2(\frac{\theta}{2})\)，化简得：\(\int_{0}^{\pi} 2a\sin(\frac{\theta}{2}) d\theta\)。此积分结果为：\(4a\)因此，心形线的全长是\(4a\)。这与直接套用面积...
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...