来自黄自成的问题
求平面曲线的长度求平面曲线x=(2/3)(t^2+6)^(3/2)且y=6t的长度,其中,tϵ[0,4].
求平面曲线的长度
求平面曲线x=(2/3)(t^2+6)^(3/2)且y=6t的长度,其中,tϵ[0,4].
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2020-03-04 09:55
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曹保亮
分别求x,y对t的导数
x'=2t*Sqrt[6+t^2]
y'=6
Sqrt[x'^2+y'^2]在[1,4]对t求积分
=Sqrt[4t^2(6+t^2)+36]=2t^2+6
求不定积分=[2t^3/3+6t]
代入上下限=200/3
2020-03-04 09:59:10
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