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Calculus/approximation to the definite integral

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Expert: - 5/9/2008


Question
Obtain an approximation to the definite integral
I = 2/√п  ∫e^-x^2 dx (integral between values 0 and 0.1)
by representing e^-x^2 using quadratic Taylor series expansion.  Comment on your answer given that
I = erf(0.1)≈ 0.1125

Answer
The Taylor's series for e^t is sum(0 to infinity)(t^n/n!)  In this problem, t is to be -x^2.  Given this series, you can break it down and integrate each term.

I'm not sure what erf(0.1) means, but I think that's the error factor.  If the error factor is 0.1125, I think the first two terms of the Taylor's series (n=0,n=1) should do it for you.  In fact, isn't the term at n = 1 smaller than 0.1125?  The first term might do it, if this is what this means, and that is why I'm not sure.

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