设f(t)为连续函数,L为分段光滑的闭曲线,证明：∮f(xy)(ydx+xdy)=0
问题描述：
设f(t)为连续函数,L为分段光滑的闭曲线,证明：∮f(xy)(ydx+xdy)=0
答
P = x³ + y²x,dP/dy = 2xy
Q = x²y + y³,dQ/dx = 2xy
∵dP/dy = dQ/dx
曲线积分与路径无关.
∴∫_(L) (x² + y²)(xdx + ydy) = 0