Calculus problem #1877

Calculus Level 3

A figure is drawn on the x-y plane. Each point $$(x,y)$$ on the figure satisfies the following equations: $$x = 3\sin \theta + 4 \cos \theta$$ and $$y = 4\sin \theta - 3 \cos \theta$$, for all $$0 \leq \theta \leq 2 \pi$$. What is the length of the figure?

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