Find the cost of painting a fence built above the given path

Reference no: EM131007989

If y : [a, b] → R² is a curve and f: R² → R is a positive function (that is f(x,y) > 0) then we can think that the scalar line ∫_γ f ds measures the one side of the area of a fence built along γ at tis base, and with height h = f(x,y) at each point ( see picture below).

340_one side of the area of a fence built.png

Use this interpretation to find the cost of painting (one side of) a fence built above the path γ{t) = (10 cos³t/, 10 sin³t), t ∈ [0, π/2], with height f(x, y) = 1 + y/3. All the units are in meters and it costs $ 5 per m² to paint the fence.

Reference no: EM131007989

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