We have to calculate Integrate[e^(-x^2),{x,0,0.1}] using series theory. Any help?

Thanks!

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- Nov 5th 2006, 01:50 AMjmytilSeries integration
We have to calculate Integrate[e^(-x^2),{x,0,0.1}] using series theory. Any help?

Thanks! - Nov 5th 2006, 04:43 AMCaptainBlack

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