Confused on Solving a Series Computation: Help Needed!

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Homework Help Overview

The discussion revolves around computing a series with a specified accuracy of 0.001, specifically related to the Maclaurin series for the function e^(-x^2). Participants express uncertainty about the initial steps and methods to approach the problem.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss whether to integrate first or focus on the series. There are suggestions to derive the Maclaurin series and to consider the series in expanded form. Questions arise about handling the series term by term and the implications of using an alternating series.

Discussion Status

Some guidance has been provided regarding the use of the Maclaurin series and the importance of writing the series in expanded form. Participants are exploring different interpretations of how to proceed with the series computation.

Contextual Notes

There is mention of the requirement to achieve a specific accuracy and the challenge of working with LaTeX for mathematical expressions. Participants are also considering the convergence properties of the series.

intervade
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Ok it says I am to computer using a series accurate to within 0.001.
gif.latex?\int_{0}^{1}x^2e^{-x^2}.gif


I'm really not sure where to start. Do I integrate this first by parts? Or am I thinking about this too much? Could someone point me in the right direction please! Help would be much appreciated!
 
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intervade said:
Ok it says I am to computer using a series accurate to within 0.001.
gif.latex?\int_{0}^{1}x^2e^{-x^2}.gif


I'm really not sure where to start. Do I integrate this first by parts? Or am I thinking about this too much? Could someone point me in the right direction please! Help would be much appreciated!
The key word is series here. Get the Maclaurin series for e-x2, and then multiply it by x2. Does that give you a place to start?
 
Ok let me just make sure I'm on the right track..

34zkmzb.jpg


Is this correct to say?

sorry, my latex skills are bad.
 
No, write the series in expanded form, not in closed form. Notice that because you have an alternating series, the error is less in absolute value than your first unused term.

Your LaTeX looks pretty good!
 
Hmm I'm not exactly sure what to do with this still. How do I integrate an expanded form of a series?
 
Term by term. This series converges pretty quickly, so you shouldn't need a whole lot of terms.
 

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