∵ds＝ x′2(t)+y2(t) dt= sin2t+(1?cost)2 dt＝ 2(1?cost) dt=2sin t 2 (0≤t≤2π)∴S＝ ∫ x′2(t)+y2(t) dt＝ ∫ 2sin t 2 dt=?4cos t 2 | ＝8
