I was having trouble with this problem:

Use a power series to approximate the value of the integral with an error less than 0.0001. Assume that the integrand is defined as 1 when x=0.

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- May 3rd 2008, 10:40 AMdark_knight_307URGENT, NEEDED BY 3:30! Power Series and error.
I was having trouble with this problem:

Use a power series to approximate the value of the integral with an error less than 0.0001. Assume that the integrand is defined as 1 when x=0. - May 3rd 2008, 11:01 AMTheEmptySet
- May 3rd 2008, 11:41 AMdark_knight_307
I'm confused about how you create the MacLauren Series though, because I'm having difficulty coming up with the derivatives of f(x).

- May 3rd 2008, 12:40 PMo_O
I think using geometric series would be the way to go because finding the derivatives of arctan(x) and generalizing looks like it's going to be a pain.

Recall the geometric series:

Looking at the derivative of arctan(x), we have which resembles the geometric series with

This gives us:

Integrating gives you the power series for arctan(x), then the rest follows as TheEmptySet showed you.

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If you need to find the maclaurin series for arctan x by finding all the derivatives, it's done here: Maclaruin Series (Scroll down a bit)

Gets messy ...