I need to calculate the volume from rotating f(x) around y=2x using Pappus–Guldinus theorem. For that I need to know the distance A.
$$L = (f(x) - 2x) / 2$$
But how can I optain the distance A?
2026-04-04 13:38:50.1775309930
Calculate rotational volumes
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A is the component of the vector $(0,L)$ perpendicular to the $y=2x$ line, i.e. in the direction given by $\mathbf{v} = \dfrac{1}{\sqrt{5}}(-2,1)$, so
$A = \big|{(0,L) \cdot \mathbf{v}}\big| = \Bigg|{(0,L) \cdot \dfrac{1}{\sqrt{5}}(-2,1)}\Bigg| = \dfrac{L}{\sqrt{5}} = \dfrac{f(x) - 2x}{2\sqrt{5}}$