为自己加油

计算上∫_Lydx+zdy+xdz，其中L是空间曲线x=cos，y=sint，z=t(0≤t≤2π)

∫_Lydx+zdy+xdz =∫₀^2π[sint(-sint)+t•cost+cost•1]dt =-(1/2)∫₀^2π(1-cos2t)dt+∫₀^2πtdsint+sint∣₀^2π =-(1/2)t∣₀^2π+1/4∫₀^2πcos2td2t+tsint∣₀^2π- ∫₀^2πsintdt+0 =-π+(1/4)sin2t∣₀^2π+0+cost∣₀^2π =-π+0+0=-π