4.13 Conclusion

Compare methods of this chapter

fx3 = function(x) exp(-x*x/2)/sqrt(2*pi)   

format(GQuad8(fx3, 0, 2), digits=22)

## [1] "0.4772498681002593223788"

format(romb(fx3, 0, 2), digits=22)

## [1] "0.4772474282947407608901"

format(trapez1(fx3, 0, 2, 12), digits=22)

## [1] "0.4770000262860045747715"

format(simps38(fx3, 0, 2, 12), digits=22)

## [1] "0.4772487626713398101153"

format(trapez1(fx3, 0, 2, 102), digits=22)

## [1] "0.4772464084452258670233"

format(simps38(fx3, 0, 2, 102), digits=22)

## [1] "0.4772498678521392978524"

format(integrate(fx3, 0, 2), digits=22)

##                                      value                                  abs.error 
##                 "0.4772498680518208469259"              "5.298537920104493984235e-15" 
##                               subdivisions                                    message 
##                                        "1"                                       "OK" 
##                                       call 
## "integrate(f = fx3, lower = 0, upper = 2)"