Integrate e^x^2, using Maclaurin rule.

In summary, the conversation is about integrating e^x^2 from 0 to 1 using Maclaurin's rule. The speaker initially encountered a problem when substituting x^2 for x in the rule, but eventually figured out a solution by using a different rule. Another person suggests using the generic Maclaurin series, but the first speaker dismisses it as it would take too long. The conversation ends with the first speaker explaining their solution and addressing a potential issue with it.
  • #1
Jarfi
384
12

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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  • #2
Why don't you compute the whole series for e^(x^2) using the generic Mac-Laurin series ?
 
  • #3
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.
 
  • #4
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.
 

FAQ: Integrate e^x^2, using Maclaurin rule.

1. What is the Maclaurin rule?

The Maclaurin rule is a method for approximating functions using a polynomial. It is a special case of the Taylor series, where the polynomial is centered at x=0.

2. How is the Maclaurin rule used to integrate e^x^2?

To integrate e^x^2 using the Maclaurin rule, we first find the Maclaurin series for e^x^2. This can be done by repeatedly differentiating the function and evaluating it at x=0. Then, we integrate the series term by term, and the resulting polynomial will serve as an approximation of the integral.

3. What is the benefit of using the Maclaurin rule for integration?

The Maclaurin rule allows us to approximate the integral of a function without having to know its exact form. This is useful when the function is complex or does not have an elementary antiderivative.

4. Can the Maclaurin rule be used for any function?

No, the Maclaurin rule is most effective for approximating integrals of analytic functions, which are functions that can be expressed as a power series. It may not work well for functions with singularities or non-analytic behavior.

5. Are there any limitations to using the Maclaurin rule for integration?

Yes, the Maclaurin rule is an approximation and may not give an exact answer. The accuracy of the approximation depends on the number of terms used in the series. Additionally, the Maclaurin rule is only valid for a specific interval around x=0, so it may not be applicable for integrals over a larger interval.

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