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10 cards from this deck
s=∫x1x21+(dydx)2 dxs = \int_{x_1}^{x_2} \sqrt{1 + (\frac{dy}{dx})^2} \, dxs=∫x1x21+(dxdy)2dx
s=∫(dxdt)2+(dydt)2dts = \int \sqrt{(\frac{dx}{dt})^2 + (\frac{dy}{dt})^2} dts=∫(dtdx)2+(dtdy)2dt
S=2π∫y1+(dydx)2dxS = 2\pi \int y \sqrt{1 + (\frac{dy}{dx})^2} dxS=2π∫y1+(dxdy)2dx
S=2π∫y(dxdt)2+(dydt)2dtS = 2\pi \int y \sqrt{(\frac{dx}{dt})^2 + (\frac{dy}{dt})^2} dtS=2π∫y(dtdx)2+(dtdy)2dt
Surface area includes the 2πy2\pi y2πy factor
(δs)2=(δx)2+(δy)2(\delta s)^2 = (\delta x)^2 + (\delta y)^2(δs)2=(δx)2+(δy)2 (Pythagoras)
111
12(cosh2x+1)\frac{1}{2}(\cosh 2x + 1)21(cosh2x+1)
12(cosh2x−1)\frac{1}{2}(\cosh 2x - 1)21(cosh2x−1)
Frustum (truncated cone)
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