Area Of Teardrop Shaped Region

Calculus Level 3

The teardrop shaped region in the image is bounded by the curve γ:[0,2π]R2\gamma:[0,2\pi] \to \mathbb{R}^2 with γ(t)=(sin(t),(tπ)2π2)\gamma(t) = (\sin(t), (t-\pi)^2 - \pi^2). What is the (unsigned) area of the teardrop shaped region?

Teardrop shaped region given by parametric equations. Teardrop shaped region given by parametric equations.

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