integrate(arctan(x^2)) from 0--->1 with finding a numerical serie,what is the value which makes the error smaller than 0,0001??

thanks for,ı need this as soon as possible.

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- Nov 21st 2008, 02:03 PMsah_mata question about power series
integrate(arctan(x^2)) from 0--->1 with finding a numerical serie,what is the value which makes the error smaller than 0,0001??

thanks for,ı need this as soon as possible. - Nov 21st 2008, 02:18 PMMathstud28
We know that

So

So since and a power series is uniformly covnergent and integrable on the interior of its IOC we have that

Now to find the appropriate error note that if and that

So the error of your series is less than or equal to the first neglected term, so calculate