Can somebody tell me what I did wrong.
The top problem is what I was given, I am sopposed to change the order of intergration.
The two double intergrations are not the same, where did I mess up?
Look at the beautiful hand drawing below.
We will consider this as a region of the II type.
We find the left and right curves.
Left curve is,
$\displaystyle x=\ln y$
The right curve is,
$\displaystyle x=3$
The bottom curve is,
$\displaystyle y=1$
The top curve is,
$\displaystyle y=e^3$
Thus,
$\displaystyle \int_1^{e^3} \int_{\ln y}^3 2 dx dy$