University:
Swansea University
Course:
MA-252 | Probability Theory
Academic year:

2023
Views:

243

Pages:

4
Author:

Amal J.

Numeric IntegrationTrapezoidal Rule.xnS f(x) dx = h 2 [cyotynt 2 (yit Y2+yn-1)noanhalSum of 1st and lastieS fix) dx =2ordinate +2 ( Sum ofintermediate ordinate)no.SdxQ.1Evaluateusing trapezoidal1 + x 2Hencedeterminerule with h 0.2the value of y.h=0-2D.801y= f(x) =14 x ,720.120140.60.8 1.0.0I.x0.860.730.600.5y10.96ByTrape zoidal RuleSdn = 0.2(++.0)++2(0.96+10.86 +tx020.73 +0.60) dx114x2 0.7837DQ.to find the value of yby actual integrationisdxtart x x]1 x x 2TT-2brs4dombequatingdiand 2ITis= 0.7837struson]4II = 53.1348allow3/11,-MNDVQ.Evaluate-x2dx by dividingthe range into 4 equal Partsusing trapezoidal orule-x2y= Q je.dph =24 0 '/40.25portS.OofaCo x00.250.50.7510.930.770.560.36yI006By Trapezoidal Rule,2ldx = 0.25(1+0.36)sp20+2 (0 - 93 +0077+0.56) ]=0.1251.36+ 4.52]JGo> 0.7352020=10.74dxQ.by trapezoidal04x+5rule by using coordinates.y=,4x+5h5-1 O = 5/11 = 0.4511=0.5x0!(0.51.522.533.54y1/50.1420.110.090.0760.060-05-05-05-0-04=0.2 4.550.0430.04LPsB,,By Traperoidal ruleS5,dx 20.54x+5 2/0(2-2+0-04)OT2/0.192to.111+d8.1+0.09+0.076REFISE+0.06ofTO+0.058+0.052gd+0.947colonibroad2+10A11stur+0.043)= 10.25 0.24+of1.35811/20.40