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# what is going wrong? watch

1. what is:

where

Using the parametrization gives the solution as .

However; Using the parametrization gives the solution as .

Should they not be the same?
2. (Original post by user6)
what is:

where

Using the parametrization gives the solution as .

However; Using the parametrization gives the solution as .

Should they not be the same?
has two branches. When you change parameterisation you are also changing the branch (assuming you are taking ).
Your second answer is correct for what is usually taken to be the principle value.
3. (Original post by Nebula)
has two branches. When you change parameterisation you are also changing the branch (assuming you are taking ).
Your second answer is correct for what is usually taken to be the principle value.
I not sure I understand you? How does changing the parametrization change the branch?
4. (Original post by user6)
I not sure I understand you? How does changing the parametrization change the branch?
Do you understand why you need a branch cut in the complex plane when trying to evaluate the integral of ?

You won't get the same answer for your integral if you use different ranges for the parameterisation angle - that's the point
5. (Original post by user6)
I not sure I understand you? How does changing the parametrization change the branch?
have you come across branch cuts?
6. (Original post by davros)
Do you understand why you need a branch cut in the complex plane when trying to evaluate the integral of ?

You won't get the same answer for your integral if you use different ranges for the parameterisation angle - that's the point
So the positive real axis is a branch cut right? I not really sure why i need a branch cut though? I thought different parametrization should give the same answer?

(Original post by TeeEm)
have you come across branch cuts?
yes, I have never used them in practice though and I am a bit confused
7. (Original post by user6)
So the positive real axis is a branch cut right? I not really sure why i need a branch cut though? I thought different parametrization should give the same answer?

(
As Nebula mentioned, the usual convention is to take a branch cut along the negative real axis and let theta (or t or whatever) range from to .

You cannot allow your function to cross a branch cut - think about what happens to the value of the function if you could!
8. (Original post by davros)
As Nebula mentioned, the usual convention is to take a branch cut along the negative real axis and let theta (or t or whatever) range from to .

You cannot allow your function to cross a branch cut - think about what happens to the value of the function if you could!
This is what is confusing me? How do I decide on a branch cut e.g. why the negative real axis and not the positive real axis. I know this is a simple case - this is the easiest example I could think of where this problem is present - more generally how do I decide on a branch cut?
9. (Original post by user6)
So the positive real axis is a branch cut right? I not really sure why i need a branch cut though? I thought different parametrization should give the same answer?

yes, I have never used them in practice though and I am a bit confused
when you have fractional powers or logs you have a branch cut starting from the branch point (here z=0) all the way to infinity
so different parameterizations produce different answers depending where the cut is

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