Did the author make a mistake in integrating by parts?

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Homework Help Overview

The discussion revolves around a potential mistake in the integration by parts process as presented in a video. The original poster questions a specific simplification involving the expression x/2 and its transformation to 2x, expressing confusion over the justification of this step.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the transformation of the expression x/2 to 2x, with some questioning the mathematical validity of the steps involved. There is a focus on understanding the role of the coefficient 1/4 in the simplification process.

Discussion Status

The discussion is active, with participants clarifying their understanding of the mathematical expressions involved. Some guidance has been provided regarding the manipulation of the terms, although there remains a lack of consensus on the justification of certain steps.

Contextual Notes

Participants express uncertainty about the solution manual's explanations and the specific steps taken in the video, indicating a need for further clarification on the integration by parts method.

bobsmith76
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Homework Statement



Screenshot2012-02-09at41900AM.png


In this video from which there is a screen shot above the author went from x/2 to 2x and all he said was half is two quarters. right a half is two quarters it is not 2. I just want to make sure that he made a mistake because I've been seeing some real bizarre things in the solution manual re integration by parts that i do not understand. everything else in the above simplification i understand except how

x/2 cos becomes 2x cos
 
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Notice the [itex]\frac{1}{4}[/itex] outside the bracket? [itex]\frac{x}{2} cos[/itex] becomes [itex]\frac{1}{4}(2x*cos[/itex]
 
I would think 1/4 * x/2 would make x/8.
 
bobsmith76 said:
I would think 1/4 * x/2 would make x/8.
Indeed. Look at what I wrote, again. Let me rephrase it: [itex]\frac{x}{2} cos[/itex] = [itex]\frac{1}{4}(2x*cos[/itex]
 
are you saying somehow they got (x/2)/(1/4). That would make 1/2 * 4, but I don't see how that move is justified.
 
Sourabh N said:
Indeed. Look at what I wrote, again. Let me rephrase it: [itex]\frac{x}{2} cos[/itex] = [itex]\frac{1}{4}(2x*cos[/itex]

bobsmith76 said:
are you saying somehow they got (x/2)/(1/4). That would make 1/2 * 4, but I don't see how that move is justified.

Nope! In the first step they have [itex]\frac{x}{2}[/itex]. right?
In the second step, they have [itex]\frac{1}{4}2x[/itex]. right?
Now, [itex]\frac{x}{2}[/itex] = [itex]\frac{1}{4}2x[/itex]. right?
 
Ok, I got it. Thanks. Sorry for being so hard-headed
 
Happens :smile: You're welcome!
 

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