Integrate e^x^2, using Maclaurin rule.

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Homework Help Overview

The problem involves integrating the function e^(x^2) from 0 to 1 using the Maclaurin series expansion. The original poster expresses confusion regarding the application of the Maclaurin rule and the resulting terms in their calculations.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the use of the Maclaurin series for e^(x^2) and question the original poster's approach to substituting x^2 into the series. There are inquiries about the feasibility of computing the entire series and concerns about time constraints for project submission.

Discussion Status

The discussion is ongoing, with participants providing suggestions for alternative approaches to the problem. Some express skepticism about the original poster's method and raise questions about the validity of pulling factors out of the integral. There is no clear consensus on the best approach yet.

Contextual Notes

Participants note the urgency of the project deadline, which may be influencing the discussion and the original poster's approach. There is also mention of confusion regarding notation, specifically the term e^(öx^2), which is not clearly defined.

Jarfi
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Homework Statement



I am suppost to integrate e^x^2 from 0 to 1 and such, I using Maclaurins rule, I got e^x=1+x/1!+x^2/2!+...+x^n/n!+e^(öx)*x^n+1/(n+1)!, 0<ö<1.

But when I put in x^2 instead of x, I end up with a legit thing except e^(öx^2)x^n+1/(n+1)! and this is giving me e^x^2 again!
 
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Why don't you compute the whole series for e^(x^2) using the generic Mac-Laurin series ?
 
dextercioby said:
Why don't you compute the whole series for e^(x^2) using the generic Mac-Laurin series ?

would take eons, got to give the project in before 8 am morning ! anyways I figured it out, writing the "leftover" part using some rule that allowed me to take the e^ö^x^2 outside the integral.
 
Jarfi said:
would take eons, got to give the project in before 8 am morning !
No, it wouldn't take "eons". Just replace x with x2 in the Maclaurin expansion for ex. It could be you're thinking you have to take a bunch of derivatives - not so.
Jarfi said:
anyways I figured it out, writing the "leftover" part using some rule that allowed me to take the e^ö^x^2 outside the integral.
First off, I don't know what e^ö^x^2 is supposed to be, especially with what renders for me as an o with an umlaut.
Second, if you're integrating a function of x, you can't just pull out a factor that has x in it.
 

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