PX275 - D3d - area of an ellipse

\begin{aligned} x & = a \cos ϕ \\ y & = b \sin ϕ \\ 0 \leq ϕ \leq 2 π \end{aligned}

taking the differentials of $x$ and $y :$

\begin{aligned} d x & = - a \sin ϕ d ϕ \\ d y & = b \cos ϕ d ϕ \end{aligned}

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