Lengths and Surface Areas (AQA A-Level Further Maths): Flashcards

$s = \int_{x_1}^{x_2} \sqrt{1 + (\frac{dy}{dx})^2} \, dx$

$s = \int \sqrt{(\frac{dx}{dt})^2 + (\frac{dy}{dt})^2} dt$

$S = 2\pi \int y \sqrt{1 + (\frac{dy}{dx})^2} dx$

$S = 2\pi \int y \sqrt{(\frac{dx}{dt})^2 + (\frac{dy}{dt})^2} dt$

Surface area includes the $2\pi y$ factor

$(\delta s)^2 = (\delta x)^2 + (\delta y)^2$ (Pythagoras)

$1$

$\frac{1}{2}(\cosh 2x + 1)$

$\frac{1}{2}(\cosh 2x - 1)$

Frustum (truncated cone)