计算曲线积分∫xdx/π+(y-x)dy,其中曲线C为摆线x=a(t-sint) y=a(1-cost)(a>0)上从O(0,0)到A(2πa,0)

显然t的取值范围就是0到2π那么原积分=∫ xdx /π +(y-x)dy=∫(0到2π) { a*(t-sint)/π * a(t-sint)' +[a*(1-cost) -a*(t-sint)] *a(1-cost)' } dt=∫(0到2π) [a*(t-sint)/π * a(1-cost) +(a-a*cost -at +a*sint)...