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<h1>Encontrando el área bajo una curva paramétrica</h1>
$$A = \int\limits_a^b {y\left( t \right)\,} x'\left( t \right)dt$$
$$A = \int\limits_0^{2\pi } {\left( {1 - \cos t} \right)\,} \left( {1 - \cos t} \right)dt$$
$$A = \int\limits_0^{2\pi } {\left( {1 - 2\cos t + \frac{{1 + \cos 2t}}{2}} \right)\,} dt$$
$$A = \int\limits_0^{2\pi } {\left( {\frac{3}{2} - 2\cos t + \frac{{\cos 2t}}{2}} \right)\,} dt$$
$$A = \left. {\frac{3}{2}t - 2sent + \frac{{sen2t}}{4}} \right|_{t = 0}^{2\pi } = \boxed{3\pi }$$
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