# Thread: Vector Calculus problem

1. ## 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.

Thanks!

2. 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?

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

After first intergating wrt y you're left with a very doable integral in x.

3. 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.

Thanks!
Here is your region of integration.

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

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

I'm too slow

4. Originally Posted by TheEmptySet
Here is your region of integration.

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

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

I'm too slow
Only because I didn't include a beautiful diagram