# Thread: Double Integral Help

1. ## Double Integral Help

I have a question in my Prob & Stat course that deals with double integration, and it's been two years since Calc III and I really don't remember exactly how to solve one. Here's the question:

The first part isn't really a double integral, but will eventually lead to one:

Integral ( xe^(-x(1+y) ) ) dy

Essentially, I am not sure how to integrate that for y. The bounds don't really matter in this case, I need to know the y-integration.

To anyone who can help, it'd be much appreciated. Thanks.

2. Originally Posted by GmasterFlash13
I have a question in my Prob & Stat course that deals with double integration, and it's been two years since Calc III and I really don't remember exactly how to solve one. Here's the question:

The first part isn't really a double integral, but will eventually lead to one:

Integral ( xe^(-x(1+y) ) ) dy

Essentially, I am not sure how to integrate that for y. The bounds don't really matter in this case, I need to know the y-integration.

To anyone who can help, it'd be much appreciated. Thanks.
Your integral is:
Int(dxdy*xe^(-x-xy)) = Int(dx*xe^(-x) * Int(dy*e^(-xy)) )
where I have split the integral into components.

The second integral (the one you are interested in) can be simply done by assuming x is a constant (it doesn't vary as y varies anyway), so
Int(dy*e^(-xy)) = 1/(-x) * e^(-xy)
where I have neglected the integration constant.

-Dan