How does du replace the circled part of the question in this integral?

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Homework Help Overview

The discussion revolves around understanding the substitution of variables in an integral, specifically how the differential du relates to a circled part of the integral expression. The subject area is calculus, focusing on integration techniques and variable substitution.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore how the expression for du is derived and its relationship to the original integral. There are attempts to clarify the substitution process and the role of dx in the context of the integral.

Discussion Status

Some participants have provided insights into the relationship between du and the circled part of the integral, suggesting that the expression can be manipulated to show how du replaces that part. There appears to be a productive exchange of ideas, with at least one participant expressing understanding following the discussion.

Contextual Notes

There are references to specific equations and expressions that are not fully detailed in the posts, which may limit the clarity of the discussion for those not privy to the original images shared. The nature of the homework context implies that participants are working within specific guidelines for problem-solving.

november1992
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Homework Statement



http://img528.imageshack.us/img528/356/hwhelp.png

Homework Equations



http://img407.imageshack.us/img407/3696/uanddu.png

The Attempt at a Solution


This is the answer I got. I was wondering how du replaces the circled part of the question.

http://img546.imageshack.us/img546/8975/hwanswer.png
 
Last edited by a moderator:
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I just came up with this information now. Is it right?

http://img851.imageshack.us/img851/3763/uandupart2.png
 
Last edited by a moderator:
november1992 said:

Homework Statement



http://img528.imageshack.us/img528/356/hwhelp.png

Homework Equations



http://img407.imageshack.us/img407/3696/uanddu.png

The Attempt at a Solution


This is the answer I got. I was wondering how du replaces the circled part of the question.

http://img546.imageshack.us/img546/8975/hwanswer.png

You have
[tex]du = \frac{e^{\sqrt{x}}}{2\sqrt{x}}dx = \frac{1}{2\sqrt{x}e^{-\sqrt{x}}}dx[/tex]

The part you have circled (and including dx) is 2du.
 
Last edited by a moderator:
Thanks, I get it now.
 

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