i am tryaing to find the integral of "e" raise to power "x" square. by conventional method by dividing e^x^2 with derivative of the power of "e" i.e. "2x". But i am not confident on my answer. Please tell me am i right???:surprised
What confidence do you have that finding the antiderivative of the laplace transform of f(t) with respect to s then inverse laplace transforming it would give you the antiderivative of f(t)? Even if it did, I would wager that you wouldn't be able to do the resulting inverse laplace transform in terms of elementary functions!I was wondering if it would in fact be possible to express the integral of e^(x^2) in terms of elementary functions. Couldn't I just use a bilateral Laplace transform on e^(x^2) and convert it into the s domain. Then, I would integrate with respect to s (since switching functions from the time domain to the s domain makes it linear, thus making it easy to integrate), and then convert that function back to the time domain using the Bromwich Integral?
An approximation with this particular function where the terms increase for real [itex]x[/tex], makes any such process largely meaningless.Correct me if I am wrong, but can't you integrate the series expansion of e^x^2 term by term? Using numerical methods, the area under the curve of e^x^2 is very close to about 6 iterations of the term-by-term integration of the series.
Why would you think that changing from t2/2 to t2 would make a difference in integrating? A simple subtitution can obviously change either one into the other. If one cannot be integrated in terms of elementary functions, the other clearly cannot either.I know it sounds like a stupid question but, instead of setting f(t)=e^(-t^2/2), why can't we set it to be e^(t^2), and see if we can integrate its Laplace transform (since e^(-t^2/2) is completely different from e^(t^2))? I especially pose this problem to Mute.
That is definitely an option; however, we do not regard an infinite power series as a nice anti-derivative, nor as a finite combination of elementary functions.How about integration using summation of (x^n)/n! ?