Question

1. (Program) Evaluate f e dr using the rectangle rule (mid-point rule), the trapezoid rule, and the two-point Gauss quadrature rule with various values of Ar. Since the error estimates have the form ElCAr" you should be able to computationally verify them by observing log El logC +plogAr and plotting log|E versus logAr to estimate p.

Answer 1

Salution iven eapuabron Evalunte Rebinle ade (mid nt ule Hese fe let AXO.2 M b-a o.2 M 5 30.6 0.8 dx

f(a-)oS ]+ (-xfC0st2,+%) 0.2f (os x0)+0.)f (o.5 x0-)+02f(0.5x1) .2 (0.5 0.2x f Co.5x1-8 d = +o 02(o.0+ (o3)+ flo.s)+fl0-)+ f (0. o. = 0.2\1.ioS1?+ 1.3498t1.6487+ 2.0137 2-4590 2 [8-563

Actual solution e-l =O.00286ou6546 guitable hexe coith Somo Dhe trapersid ule 2 e' 1 e 1.724006 2 0.0231 Here P Shoco thet Grauss yuatto e ule Here e d pC

(W) osker - e edx +- dz e da e 8 tE 9Z 8 t 1t'

E - Exo So lE Ca with sme sulbuble fex e