JEE Advance - Mathematics (2001 - No. 8)
Let $$b \ne 0$$ and for $$j=0, 1, 2, ..., n,$$ let $${S_j}$$ be the area of
the region bounded by the $$y$$-axis and the curve $$x{e^{ay}} = \sin $$ by,
$${{jr} \over b} \le y \le {{\left( {j + 1} \right)\pi } \over b}.$$ Show that $${S_0},{S_1},{S_2},\,....,\,{S_n}$$ are in
geometric progression. Also, find their sum for $$a=-1$$ and $$b = \pi .$$
the region bounded by the $$y$$-axis and the curve $$x{e^{ay}} = \sin $$ by,
$${{jr} \over b} \le y \le {{\left( {j + 1} \right)\pi } \over b}.$$ Show that $${S_0},{S_1},{S_2},\,....,\,{S_n}$$ are in
geometric progression. Also, find their sum for $$a=-1$$ and $$b = \pi .$$
The sequence S_0, S_1, S_2, ... S_n is an arithmetic progression.
The sequence S_0, S_1, S_2, ... S_n is a harmonic progression.
The sequence S_0, S_1, S_2, ... S_n is a geometric progression with a common ratio of e.
The sequence S_0, S_1, S_2, ... S_n is a geometric progression with a common ratio of 1/e.
The sequence S_0, S_1, S_2, ... S_n is not a progression.
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