Question: 6. The error function erf(x) y=erf(x)=20xet2dt arises often in many fields of engineering because the integrand is a scaled and recentered form of the Gaussian

6. The error function erf(x) y=erf(x)=20xet2dt arises often in many fields

6. The error function erf(x) y=erf(x)=20xet2dt arises often in many fields of engineering because the integrand is a scaled and recentered form of the Gaussian distribution (the famed "bell-shaped curve"). A limit of y=1 is reached in the limit of x (by a subtle analytic solution), but for finite x the integral must be calculated numerically. (a) Estimate the value of erf(1) using the trapezoidal rule with 10 intervals (11 points). Call this estimate I2. (b) Estimate the value of erf(1) using Simpson's 1/3 rule, with the same 11 points. (c) Estimate the value of erf(1) using the trapezoidal rule with only 5 intervals (6 of the prior points). Call this estimate I1. (d) Use Romberg integration to combine your estimates I1 and I2 into an even better estimate, I3, by using I3=34I231I1

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