help with double integrals

[remote musk]

hi i need help with understanding double integrals. can someone help?
evaluate the double integral:

[wicked ore]

1. Wait patiently for a helper to come along.
2. Once someone helps you, say thank you and close the thread with:

+close

3. Feel free to nominate the person for helper of the week in #helper-nominations
4. Do not ping the mods, unless someone is breaking the rules.
5. If you're happy with the help you got here, and the server overall, you can contribute financially as well:

[signal robin]

Try drawing a picture first, then you'll see the region.

[remote musk]

i got this but i dont know which bounds to use

[signal robin]

As for the x-limits, equate those two quadratic functions, then you'll be able to find them.

[remote musk]

i see, i think i got it

[signal robin]

Great! You can show your result, I'll check it.

[signal robin]

Something isn't right. Try substituting the y-limits more carefully.

Would probably be easier to do 2xy + y^2 = y(2x + y) first.

Then you will see that what you have is something of the form (a + 2)(b + 2) - (a - 2)(b - 2).

That is easier to simplify.

[remote musk]

i see, ill try that again
i was afraid to not mess up things but i did it anyways xd

[signal robin]

No worries! That's a possibility when there's a lot of algebra.

[remote musk]

im sorry for being slow i was kinda confused on what to do exactly

oh wait i messed up again

should be 8x^2+24x

result should be -36

[signal robin]

Yeah, I think that's correct.

[remote musk]

thanks a lot