# Real Analysis : Using a Summation Series to Estimate an Integral

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Say the only tool you have available to you is a pocket calculator which performs addition, subtraction, multiplication, and division, accurate to 15 decimal places.

Explain a practical way to compute:

Integral from 0 to 1 of e^[-(x^2)]

to within an error less than 10^-8. Prove that the method works.

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Since , we have

So,

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