We have to calculate Integrate[e^(-x^2),{x,0,0.1}] using series theory. Any help?
Thanks!
We will do this by expanding the integrand as a power series and then integrating term by term.
so:
Hence:
Now we will interchange the order of the integration and summation, which
is valid in this case but I will leave the justification for you to provide:
so:
Summing the first two terms on the right gives an estimate for the integral of 0.0996666667
compared to a fairly accurate numerical integration which gives: 0.0996676643, and the
sum of the first five terms of the series give: 0.0996676643.
RonL