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

2023
Views:

281

Pages:

5
Author:

Amal J.

TT/2 Sinx, dxQ . Evaluaterange into 6 equal parts.by 1/3 -Rule dividing theII/2Ars:y= SinxSinnh=II{-12y293yu950-11,=yo4,=211BIT4 II5TTIIOTT/12121212T22xO0.2580.50.7070.8660.9651ySimpson's0.5+ 0.866 +1Praperoided rule.+ 4II + II+22712 2S = II2D36+4A .258 +0.707++0.965]]36= 0.99111 Q. Find the value of log 2 4/3from in x2 b/x using1+x3Simpsorie1/3 rule ? h= 0.25y= x21x3h- 0.25fill O gabs 0.5 0.752142yO0.061 0.2220.3950.5raidBy trapesimpsons rule1.015S0.2501+x33060880012.0 820404 [0.061 +0.395orsturJ-3=0.0833 F2.7788NAC=0.231 =PPP se By actual integrationS'x2dx.0 B 1 x x 3put 1+migt3xdtAx2A2 Etx=SaandtTtns3x2isx 2dn1+0=0(Itns)1=t2at3x = at=dxpoto103(01 tx3)x'dx= at3.2at1/3t3= 3 logt],>3 1 [ log 2] =log 2 1/3 =0.23.()82.0 Q. . calculate $0.00 S 0.7 in ndn 2/20.5taking 5 ordinates by simpson'srule.3y= xexxh==0.7-0.520.2=0.04550412O0.040.0810.12/0.16y0its1550.20.240.280.1320.1360.4.0.44 0.480.520.560.6EVsipeE0.680.72 x0.50.540.580.62"0.660.7.y0.4280.4280.4260.423 0.4190.415simpon's rule is50-7 ex 12 dx0.5HayR 0.040.428-+0.415)3+2 (0.426.70.419) t+14[0.428+Ellage0.423]=0.013couryget 2PE0.07718Q. EvaluateS 5-2 lognidnby4wistom1)trapezoidal rule2) 8irthponsor's rule withexact valuest3)compare I ith= = 0.2.givenUA.-2to