Question

How do I change the order of integration for the following equation...(i'll use the equation editor below)

Answer 1

\[I=\int\limits_{0}^{\pi/2}\int\limits_{x}^{\pi/2} [(\sin y) / (y)] dy dx\]

Answer 2

my solution is the following:
if we draw the area of the integral, we can see it's bounded by the lines:
\[x=y, x=0, y=\pi/2\]
so x changes from \[x=0 \to x=y\], and we can fix y as \[y=0 \to y=\pi/2\]
the integral I will be as:
\[I=\int\limits_{0}^{\pi/2}\int\limits_{0}^{y}(siny/y)dxdy\]
which will result in a value \[I=1\]