Integration by Parts & Change of Variables Proof

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Homework Help Overview

The discussion revolves around the proofs of Integration by Parts and the Change of Variables formula, specifically referencing a book and concerns about potential typographical errors in the provided proofs.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to clarify their understanding of the proofs and seeks feedback on their rewrites, questioning specific elements like the inclusion of g_{i-1}. Other participants suggest alternative methods, such as integrating the product rule or using the fundamental theorem of calculus, to approach the problem.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations and approaches to the proofs. Some guidance has been offered regarding alternative methods, but there is no explicit consensus on the correctness of the original poster's rewrites or the presence of errors.

Contextual Notes

The original poster expresses uncertainty about their rewrites and the potential for typographical errors in the book, indicating a need for clarification on specific terms used in the proofs.

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I'm just curious about the proofs of Integration by Parts & the Change of Variables formula
as given in this book on page 357. I think there are a lot of typo's so I've uploaded my
rewrite of them but I am unsure of how correct my rewrites are. If someone could point
out the errors & why I made them I'd really appreciate it as I don't see how I messed up
but still feel I did, for example I'm not sure whether the g_{i-1} is a typo in
the last lines of the IBP proof, when the author takes the norm of the partition to zero.
I can't see how it's included according to my rewrite :confused:

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For integration by parts, why not just integrate the product rule for differentiation?
 
The challenge I suppose. So no errors?
 
I don't see why you just done use the fundamental theorem of calculus. That's what we did in our analysis course.
 

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