Mathematics

Problem

Let

b \neq 0

and for

j=0, 1, 2, \dots, n

. Let

S_j

be the area of the region bounded by

Y

-axis and the curve

x \cdot e^{ay} = \sin by

\frac{j\pi}{b} \le y \le \frac{(j+1)\pi}{b}

. Show that

S_0, S_1, S_2, \dots, S_n

are in geometric progression. Also, find their sum for

a = -1

and

b = \pi