高数微积分题一道The base of a circular fence with radius 10 m is giv

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高数微积分题一道The base of a circular fence with radius 10 m is given by x = 10 cos t; y = 10 sin t.Theheight of the fence varies from 3 m to 5 m such that,at position (x,y),the height is given bythe function h(x,y) = 4 + 0.01(x2 -y2).Suppose that 1 litre of paint covers 100 m2.Sketchthe fence and determine how much paint you will need if you paint both sides of the fence.Ans:5 litre请具体讲一下思路,万分感激!

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知性的巨人

重要的巨人

2026-03-31 20:22:02

如图进行微分。微元面积等于高度h乘以微元弧长。dS=h*dl=h*R*dθ所以S=∫Rhdθ(积分范围从0到2π) =∫10*(4 + ((cosθ)^2 -(sinθ)^2))dθ剩下的你会算了吧

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  • 狂野的书本
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    2026-03-31 20:22:02

    如图进行微分。微元面积等于高度h乘以微元弧长。dS=h*dl=h*R*dθ所以S=∫Rhdθ(积分范围从0到2π) =∫10*(4 + ((cosθ)^2 -(sinθ)^2))dθ剩下的你会算了吧

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