计算上∫Cyds，其中L为：x=a(t-sint)，y=a(1-cost)(0≤t≤2π)．
因为dx/dt=a(1-cost)，dy/dt=asint ds=√[(dx/dt)2+(dy/dt)2n]dt=√[a2(1-cost)2+a2sin2]tdt =√2a√(1-cost)dt 所以∫Cyds=∫02πa(1-cost)•√2a√(1-cost)dt =√2a2∫02π(1-cost)3/2dt= √2a2∫02π[2sin2(t/2)]3/2)dt =4a2∫02πsin2(t/2)dt=-8a2∫02π [1-cos2(t/2)]dcos(t/2) =-8a2[cos(t/2)∣02π-(1/3)cos3(t/2)∣02π]=(32/3)a2
