Boundaries Change With U-Sub? Huh?

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Homework Help Overview

The discussion revolves around the concept of changing boundaries in the context of integration with substitution, specifically focusing on the transformation of limits from [0,2] to [1,17].

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the reasoning behind changing the boundaries during substitution in integration. Questions arise about the relevant theorem and its implications for the limits of integration.

Discussion Status

Some participants have provided insights into the relationship between the original variable and the substituted variable, while others continue to seek clarification on the underlying theorem governing these changes. There is an indication of understanding developing among some participants.

Contextual Notes

There is a mention of uncertainty regarding the specific theorem that applies to the situation, indicating a gap in knowledge that participants are attempting to address.

TranscendArcu
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So, I've been trying to figure out why the boundaries change in the example below. It seems like the boundaries change from [0,2] to [1,17] and I can't discover why this is. Ideas?

http://img841.imageshack.us/img841/3808/skjermbilde20111129kl52.png
 
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You're just making a substitution. What is the theorem that says that you can calculate integrals by substitution?? What does it say about the bounds?
 
I don't know what theorem this is. What theorem is it?
 
If u = 1+4t2, what u values correspond to your t value limits?
 
Oh! I understand this now: 4t2 + 1, where t=2,0 gives 17 and 1, respectively.

Okay. But, just out of curiosity, what theorem is this? I still don't know.
 

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