计算∫L（2a-y）dx-(a-y)dy,L；摆线x=a(t-sint),y=a(1-cost)从点O(0,0)到点B(2πa,0). 过程
问题描述：
计算∫L（2a-y）dx-(a-y)dy,L；摆线x=a(t-sint),y=a(1-cost)从点O(0,0)到点B(2πa,0). 过程
答
计算[L]∫(2a-y)dx-(a-y)dy,L；摆线x=a(t-sint),y=a(1-cost)从点O(0,0)到点B(2πa,0).原式=[0,2π]∫{[2a-a(1-cost)]a(1-cost)-[a-a(1-cost)](asint)]}dt=[0,2π]∫[a²(1-cos²t)-a²sintcost]dt=[0,2...