2 由摆线x=a(t - sint),y=a(1 -cost)的一拱（0≤t≤2∏) 与y=0所围图形的面积=∫(0,2πa)ydx=∫(0,2π)a(1 -cost)d[a(t - sint)]
=a^2∫(0,2π)(1-cost)^2dt
= a^2∫(0,2π)[1-2cost+(cost)^2]dt
=a^2∫(0,2π)[1-2cost+(1+cos2t)/2] dt
=2πa^2+0+ (2πa^2)/2+0=3πa^2
1. 由摆线x=a(t - sint),y=a(1 -cost)（a>0,t属于0~2∏）,x=0所围的均匀薄板的面积
=∫(2a,0)xdy=∫(π,2π)a(t - sint)d[a(1 -cost)]
=∫(π,2π)(a^2)*(t + sint)sintdt
=∫(π,2π)(a^2)*[t*sint]dt+(1/2)∫(π,2π)(a^2)*(1-cos2t)dt
=(3/2)πa^2