2. The error function, erf (x) = 2 et2 dt 0 x is important in probability and in

Question

2. The error function, erf (x) = 2 et2 dt 0 x is important in probability and in the theories of heat flow and signal transmission. However, there is no elementary expression for the anti-derivative of et2 , so the integral cannot be evaluated numerically. Use Simpson’s Rule with n=10 to estimate erf (1).

2. The error function, erf (x) e dt VT is important in probability and in the theories of heat flow and signal transmission. However, there is no elementary expression for the anti-derivative of e so the integral cannot be evaluated numerically. Use Simpson's Rule with n 10 to estimate erf(1).

Explanation / Answer

erf(x)=(2/)[0 to x]e-t^2 dt

erf(1)=(2/)[0 to 1]e-t^2 dt

n =10 , a=0 , b=1 , t=(b-a)/n =1/10=0.1

using simpson's rule :

erf(1)

=(2/)(0.1/3)[e-0^2+4*e-0.1^2+2*e-0.2^2+4*e-0.3^2+2*e-0.4^2+4*e-0.5^2+2*e-0.6^2+4*e-0.7^2+2*e-0.8^2+4*e-0.9^2+e-1^2]

erf(1)=0.842701

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