计算∫(x^2+y^2)ds,其中L为曲线x=a(cost+tsint),y=a(sint-tcost)

2025-05-08 12:49:34
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回答1:

dx=a(-sint+sint+tcost)dt=atcostdt
dy=a(cost-cost+tsint)dt=atsintdt
d²s=d²x+d²y=(at)²d²t ( ds=atdt ) here
x²+y²=.................
∫(x^2+y^2)ds=∫.....atdt