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Question Number 204666 by Ghisom last updated on 25/Feb/24

$$\mathrm{this}\mathrm{is}\mathrm{a}\mathrm{closed}\mathrm{curve}:$$$$f\left(\theta \right)={\left({\mathrm{e}}^{\mathrm{i}\theta }\right)}^{\left({\mathrm{e}}^{\mathrm{i}\theta }\right)}={\mathrm{e}}^{-\theta \sin \theta }{\mathrm{e}}^{\mathrm{i}\theta \cos \theta };-\pi <\theta ⩽\pi$$$$f:\{\begin{array}{l}x\left(\theta \right)={\mathrm{e}}^{-\theta \sin \theta }\cos \left(\theta \cos \theta \right)\\ y\left(\theta \right)={\mathrm{e}}^{-\theta \sin \theta }\sin \left(\theta \cos \theta \right)\end{array}$$$$\mathrm{find}\mathrm{the}\mathrm{area}$$

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