计算∫cz^3ds,其中C为圆锥螺旋线：x=tcost,y=tsint,z=t,0
问题描述：
计算∫cz^3ds,其中C为圆锥螺旋线：x=tcost,y=tsint,z=t,0
答
求导：x'＝cost-tsint,y'＝sint+tcost,z'＝1ds＝√[(x')^2+(y')^2+(z')^2]dt＝√(2+t^2)dt∫z^3ds＝∫(0到√2) t^3√(2+t^2)dt（换元u＝t^2）＝1/2×∫(0到2) u√(2+u)du＝1/2×∫(0到2) [√(2+u)^3－2√(2+u)]du,√...