approximate the integral below so that the magnitude of the error is at most 1/216

the integral from 0 to 1 of e^-x^2

I am pretty sure this is a series problem but I cannot figure out how to approach it?

thanks in advance

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- Apr 7th 2009, 11:04 PMcalculushelptxmagnitude of error
approximate the integral below so that the magnitude of the error is at most 1/216

the integral from 0 to 1 of e^-x^2

I am pretty sure this is a series problem but I cannot figure out how to approach it?

thanks in advance - Apr 8th 2009, 02:12 AMchisigma
The Taylor expansion of the 'gaussian function' is...

(1)

... and integrating it 'term by term'...

(2)

The (2) is an 'alternating terms' series, so that the error can't be greater than the first term you neglect. The condition for error then becomes...

(3)

... and that happens just for so that the first 4 tems of (2) will give the requested accuracy...

Kind regards

- Apr 8th 2009, 06:24 AMcalculushelptx
Now I see it. Thank you so much now I see where I went wrong.