A problem with Integration by Parts in Hartle's "Gravity"

In summary, the conversation is about a reader seeking guidance on a scary-looking integral in the book "Gravity" by Hartle. Another user provides a helpful explanation and welcomes the new reader to the physics forum.
  • #1
Abtinnn
58
7
Hi guys!

I am reading the book "Gravity" by Hartle. I came across this scary-looking integral. The author does integration by parts and I don't get how he does it. Could someone guide me please?

Relevant equations:

∫u dv = uv - ∫v du
 

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  • #2
Hi,
 
  • #3
Sorry - I'm new to the physics forum and posted nothing as a reply by mistake. See if this helps:

:
forum answer 001.jpg
 
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  • #4
Asher Weinerman said:
Sorry - I'm new to the physics forum and posted nothing as a reply by mistake. See if this helps:

:View attachment 80950

Wow!
Thanks a lot! It really helped!
I really really appreciate it :)

P.S. I am kinda new too. Welcome to PF :D
 
  • #5
Oops - I forgot a term in my derivation. Here is the corrected version:
physics 2 forum 001.jpg
 
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1. What is Integration by Parts and why is it important in Hartle's "Gravity"?

Integration by Parts is a mathematical technique used to solve integrals by breaking them down into smaller, more manageable parts. In Hartle's "Gravity", it is used to solve for the equations of motion in general relativity.

2. What is the specific problem with Integration by Parts in Hartle's "Gravity"?

The problem with Integration by Parts in Hartle's "Gravity" is that it does not work for all types of integrals. In certain cases, the integration by parts formula leads to incorrect results or infinite series.

3. How does the failure of Integration by Parts affect the understanding of "Gravity" in Hartle's work?

The failure of Integration by Parts can significantly impact the understanding of "Gravity" in Hartle's work. It can lead to incorrect solutions and interpretations of the equations of motion, which can affect the overall understanding of the theory of gravity.

4. Are there any alternative methods to solve the integration problems in Hartle's "Gravity"?

Yes, there are alternative methods to solve the integration problems in Hartle's "Gravity". Some examples include the use of numerical techniques, series expansions, and approximations. These methods can provide more accurate solutions in cases where Integration by Parts fails.

5. Is there ongoing research to address the problem with Integration by Parts in Hartle's "Gravity"?

Yes, there is ongoing research to address the problem with Integration by Parts in Hartle's "Gravity". Scientists and mathematicians are constantly working to develop new techniques and approaches to solve integrals in general relativity, which can help improve the understanding of "Gravity" in Hartle's work.

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