Excellent! Your angle limits are correct now. Don't they make more sense? However, I must confess to misleading you about the limits. You don't want to integrate from to , but instead you want to integrate from to what?

Your integrand still is not correct, though it's oh-so-close. Look at this expression (the exponent):

How does this simplify?

Comment: learn LaTeX! That's how I can post my questions and have the math appear right alongside text. Unfortunately, when I go into the Advanced Editing mode to do some serious math typing, I can't see the pictures you've scanned in. So I have to have an extra tab open in order to navigate to the problem so I can see your scanned images. It also takes longer to scan than to type LaTeX, once you've learned it a bit. Double-click expressions that are in LaTeX in order to see how to do things. For example: here's the code for the last integral you posted:

Code:

\displaystyle{\int_{-\pi/2}^{\pi/2}\int_{0}^{r}e^{2r^{2}}r\,dr\,d\theta},

which produces

when enclosed with the math tags (available in the Advanced Editing mode).