Consider the areas \( S_{0}, S_{1}, S_{2}, \ldots \). bounded by the \( x \)-axis and half-waves...

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Consider the areas \( S_{0}, S_{1}, S_{2}, \ldots \). bounded by the \( x \)-axis and half-waves of the curve \( y=e^{-x} \sin x \), where \( x \geq 0 \). Then Statement-I: The value of \( S_{0} \) equals \( \frac{1}{2}\left(1+e^{\pi}\right) \) sq. units. Statement-II: The sequence \( S_{0}, S_{1}, S_{2}, \ldots \ldots \ldots . \). forms a G.P. with
Statement-III: Common ratio equals is \( e^{-\pi} \) then the statments are respectively
(a) \( \mathrm{TFT} \)
(b) \( \mathrm{FFF} \)
(c) \( \mathrm{TTT} \)
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