# Vector Calculus problem

• Jun 7th 2008, 06:55 PM
Zolroth
Vector Calculus problem
I have no idea how to solve it. Obviously there is a way to get around imaginary integration. But i dont know how.

http://img444.imageshack.us/img444/3...tionrk8.th.jpg

Thanks!
• Jun 7th 2008, 08:31 PM
mr fantastic
Quote:

Originally Posted by Zolroth
I have no idea how to solve it. Obviously there is a way to get around imaginary integration. But i dont know how.
[snip]
Thanks!

Did you draw the region of integration?

$\displaystyle \int_{y = 0}^{y=1} \int_{x = 5y}^{x = 5} e^{x^2} \, dx \, dy = \int_{x = 0}^{x=5} \int_{y=0}^{y = x/5} e^{x^2} \, dy \, dx$.

After first intergating wrt y you're left with a very doable integral in x.
• Jun 7th 2008, 08:35 PM
TheEmptySet
Quote:

Originally Posted by Zolroth
I have no idea how to solve it. Obviously there is a way to get around imaginary integration. But i dont know how.

http://img444.imageshack.us/img444/3...tionrk8.th.jpg

Thanks!

Here is your region of integration.

Attachment 6687

Change the order an integrate with respect to y first to get

$\displaystyle \int_{0}^{5}\int_{0}^{\frac{1}{5}x}e^{x^2}dydx$

I'm too slow
• Jun 7th 2008, 10:38 PM
mr fantastic
Quote:

Originally Posted by TheEmptySet
Here is your region of integration.

Attachment 6687

Change the order an integrate with respect to y first to get

$\displaystyle \int_{0}^{5}\int_{0}^{\frac{1}{5}x}e^{x^2}dydx$

I'm too slow

Only because I didn't include a beautiful diagram :D