The error function, erf (x )equals startfraction 2 over startroot pi endroot endfraction integral from 0 to x e superscript negative t squared baseline dt , important in probability and in the theories of heat flow and signal transmission, must be evaluated numerically because there is no elementary expression for the antiderivative of e superscript negative t squared. a. use simpson's rule with n equals 8 to estimate erf (3 ). b. in [0 comma 3 ], startabsolutevalue startfraction d superscript 4 over dt superscript 4 endfraction (e superscript negative t squared )endabsolutevalue less than or equals 12 . give an upper bound for the magnitude of the error of the estimate in part (a). a. the simpson's rule approximation for erf (3 )is