高数打卡04

1.求心脏线r=a(1+cosθ)(a>0,0⩽θ⩽2π)所围区域之面积.1.求心脏线r=a(1+cos\theta)(a>0,0\leqslant\theta \leqslant2\pi)所围区域之面积.1.求心脏线r=a(1+cosθ)(a>0,0⩽θ⩽2π)所围区域之面积. 图形:图形:图形: S=∫02πdθ∫0a(1+cos⁡θ)rdr=12∫02πa2(1+cos⁡θ)2dθ=(12a2θ+a2sin⁡θ+14a2θ+18a2sin⁡2θ)∣02π=32πa2\begin{aligned} &S=\int_{0}^{2 \pi} d \theta \int_{0}^{a(1+\c