令x=cost,y=sint ds=(x‘)^2+(y')^2=1*dt=dt t∈[0,2π]∫[0,2π](acost+bsint)^2dt=∫[0,2π](a^2*cost^2+b^2sint^2+2absintcost)dt=∫[0,2π)(1/2*a^2(1+cos2t)+1/2*b^2*(1-cos2t)+2absintcost)dt=1/2*a^2*(2π)+1/2*b^2*(2π)+0=π(a^2+b^2)