dextercioby said:Why don't you compute the whole series for e^(x^2) using the generic Mac-Laurin series ?
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:would take eons, got to give the project in before 8 am morning !
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.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.
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.
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.
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.
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.
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.