求x轴和摆线 x=a(t-sint) , y=a(1-cost)； (0≤t≤2π)围成图形的面积
摆线一拱与x轴所围成图形的面积：
S=【0,2π】∫ydx=【0,2π】π∫a(1-cost)[a(1-cost)]dt=【0,2π】πa²∫(1-cost)²dt
=【0,2π】πa²∫(1-2cost+cos²t)dt
=【0,2π】πa²[t-2sint+(1/2)∫(1+cos2t)dt]
=πa²[t-2sint+(1/2)t+(1/4)sin2t]【0,2π】
=πa²(2π+π)=3πa²