Passage For \( j=0,1,2, \ldots n \) let \( S_{j} \) be the area of region bounded by the \( x \)....

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Passage
\( \mathrm{P} \)
For \( j=0,1,2, \ldots n \) let \( S_{j} \) be the area of region bounded by the \( x \)-axis and the curve \( y e^{x}=\sin x \) for \( j \pi \leq x \leq(j+1) \pi \)
The ratio \( \frac{S_{2009}}{S_{2010}} \) equals:
(1) \( e^{-\pi} \)
(2) \( -e^{\pi} \)
(3) \( \frac{1}{2} e^{\pi} \)
(4) \( 2 e^{\pi} \)


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