Question

Integrate Sved Vädx with n=4 using (1) Trapezoidal rule and (2) Simpson's rule, and compare with the true value.

Answer 1

Solution 8 Trade Te ftphone= (1.4 3 [235]* = { [ 8%] = { 1.22.627 = 15-0849 3/2 3/2 Ia Io 15.0849 True value / Exact value I = fx de using Trapezoidal rule n = 4 b-a ha 6=8, 20 hy step size 8=2 h = 80 4 [h=2 yo = f(n) = va x2 = 4 X-2 1928 X = 6 x 100 ly=11414 42 = 2 42=%44974 2.828 y Yo=0 CS Scanned with CamScanner

y = f(n)=√x Yo = f(0) 2 Ýi = f/2) = 12 1.414 Y2 = f (4) = 54 Y3-316) = 6 = 2.449 44 = 818) - 2.828 8 11: [19o+yn)+2(91+42 + 9n-)] +, [(9 + 9+) +2 (9 + 2 +93) 3 [10+2-828) +2(1.414 +2 +2.449)] = [ 2.828 +2 (1.419+2+ 2.949) ] 11,2 14:554 Approximate value (11 a 14.554 Ang Approximate value Error = | Truevake 1 15.0849-14:154) Error = 0.5309 Ang CS Scanned with CamScanner

(11) [2= Suda uring simpson's sule Here, we will consider simpson's Ird scele [ha 2 2020 2122 22-4 x 22=6 19-8 Yooo 411.414 Y2=2 Y3 : 2.949 44 - 2.828 11 [2= h [1 90+yn) + 2 199794+46 --Yor2 ) + 12) +4191+99+45-)] 1 (90+94) + 2192) +4 141 +93)] [ 10+2-828) +212) + 411.414+2.499) ] i [ [ 21828 +4 +4131863) ] [2 = 140853+ Appoonimate Value - 2 3 こ Any Errora | Toue value- Appoonimate value - 115.0849 - 14.853 | -0.2319 Error0.2319 CS Scanned with CamScanner Ang