hi im confused of how is it possible to get 2 different integral values just by doing change of integrals from D plane to E plane, is it because of the jacobian? because in the D plane the integral was equal to 0 and later it was equal to another number,how is this not a contradiction to the law of change of integral variables?
#double integrals
proven condor
grave scarabBOT
hi im confused of how is it possible to get 2 different integral values just by ...
- Do not ping the Moderators, unless someone is breaking the rules.
- Do not ping the Helper Moderators, unless there is a conflict between helpers.
- Do not ping other members randomly for help.
- Ask your question and show the work you've done so far. If you've posted a screenshot of a question, specify which part you need help with.
- Wait patiently for a helper to come along.
- If the Helper has answered your question, remember to thank them with the Mathematics Ranks bot and close the thread with:
+close
Feel free to nominate the person for helper of the week in #helper-nominations
If you're happy with the help you got here, and the server overall, you can contribute financially as well:
covert nebula
hi im confused of how is it possible to get 2 different integral values just by ...
Show us the original problem and your work.
Why those bounds for u and v?
proven condor
that's what i was given in the question.
covert nebula
Well, at a glance, you're integrating a circle, once in rectangular form and once in polar form, but the polar form doesn't consist of an integer number of rotations.
proven condor
but isn't D the image of E on xy plane?
covert nebula
but isn't D the image of E on xy plane?
Yes, but not under a bijective function.
proven condor
Yes, but not under a bijective function.
can you elaborate?
covert nebula
can you elaborate?
...(u, v) = (1, 1) maps to (x, y) = (-1, 0), and so does (u, v) = (1, 3).
proven condor
...`(u, v) = (1, 1)` maps to `(x, y) = (-1, 0)`, and so does `(u, v) = (1, 3)`.
so if it isn't a bijective function we get a different value for the integral?
covert nebula
so if it isn't a bijective function we get a different value for the integral?
Okay, think about it like this. An integral is signed area, right?
proven condor
yeah
covert nebula
You've got overlapping area.
proven condor
You've got overlapping area.
yeahh im still confused about all of the double integral stuff, but i'll try to think about what you said, thank you
covert nebula
yeahh im still confused about all of the double integral stuff, but i'll try to ...
If I'm right, which I might not be, it should actually be -1/4.
proven condor
i calculated it again and got -1/3
covert nebula
Maybe I'm not right, then. I'll be frank, I'm not sure how this double integral should be interpreted, I guess as a volume? But then I don't know how the overlap in the angle should be interpreted.
Actually, wait, you're only integrating x the second time.
Or, wait, I guess that's what the Jacobian is for?
proven condor
we're calculating the integral of the function x * the jacobian dudv on the second time
spare pumiceBOT
@proven condor
proven condor
Maybe I'm not right, then. I'll be frank, I'm not sure how this double integral ...
forgot to thank you bro
+close
spare pumiceBOT
Thank you for your feedback! Techie Literate has been awarded 1 
. They now have 864 . They have 3 daily left for today.