Double integrals that involve integration by parts

[jwxie]

Homework Statement

Evaluate the double integral.

Homework Equations

integral by part: uv - integral of v*du

The Attempt at a Solution

I wrote out my works. And I am just stuck at the x integration...

Please click on the links to see the pictures. I don't want to resize it which may reduce the quality.

http://i786.photobucket.com/albums/yy145/gokoproject/100702_150423.jpg
http://i786.photobucket.com/albums/yy145/gokoproject/100702_150440.jpg

I tried to break the last integration into three parts, which each had x^2 at the bottom. But then the integration by parts seem impossible...

The answer to the question is 19/2 - 1/2e^6
I am sure the first part with respect to y is correct (I verified that with wolframalpha).Any help would be appreciate. Thank you

* I believe doing dx first is easier, if I am correct. But I already started, so I just want to see how can i crack down with dy first. There can be ugly expression during exam too.

 

[Dick]

Doing it dx first is a LOT easier. If you do it dy first you need incomplete gamma functions to write down an indefinite integral (as you are discovering). There's no elementary way (like integration by parts) to do that integral.

 

[jwxie]

oh god. lol
thanks Dick. I see what you mean :)