Double integrals that involve integration by parts

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SUMMARY

The discussion focuses on evaluating a double integral using integration by parts, specifically addressing the challenges faced when integrating with respect to y first. The participant confirmed the correctness of their initial integration with respect to y using Wolfram Alpha, arriving at the answer of 19/2 - 1/2e^6. The conversation highlights the complexity of the integration process, particularly when incomplete gamma functions are involved, making the integration by parts approach more favorable for certain scenarios.

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  • Learn about incomplete gamma functions and their uses in integration
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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.
 
Last edited:
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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.
 
oh god. lol
thanks Dick. I see what you mean :)
 

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