Question

Evaluate ds using the trapezoidal rule and Simpson's rule. Determine The value of (Round to four decimal places as needed.) i. the value of the integral directly. ii. the trapezoidal rule estimate for n = 4. iii. an upper bound for ET iv: the upper bound for Et as a percentage of the integral's true value. v. the Simpson's rule estimate for n=4. vi. an upper bound for Es vii. the upper bound for Es as a percentage of the integral's true value.

Evaluate Integral from 2 to 10 StartFraction 9 Over s squared EndFraction ds using the trapezoidal rule and​ Simpson's rule. Determine

Answer 1

so we stop here. root of f(a)= o is i Kg - 1.96875 She au s® fla) ds - - fla) - acq';b-10 i Direct integral Scanned with CamScanner

2 = 49) (+). =(-9) ( +) = (-9) (-0.4) = 3.6 2 (ii) Trapezoidal rule is T(n) = x [ f(x) + 2 f(x) + df{*)+ -- +2f1*»)+ szzbaleno AX- b-a п Here n = 4 10-2 - 2 A35 is sx = 1022 20 = 2 = 2 ; f() = f(2)= 2:25 94 = 20 FAX=4 ; f(3) = f(4)= 0.5625 My = y +sx = 6 ; flex) = FO)= 0.25 1 = x + 2y = : 3(x) = f(z) = 6-14 0 625 cs gegaano #4X = 10 i fl*4)= f(0) = 0.09 CtimScanner

.:7(4) = b[ { flio) +&£(4) + 2 f(49) + 8f12y) + f(x)] 2 2.25 + 2x 0.5625 + 2x 0.25 + 2x0.140625 +0:09] - 4.24625 duni) 151. 16-a3ex 12 na where K = Max XE[a, b] f'(s) = 9(-1) 53 {"(5) = 9(-1) (-3) 54 :: f'() = f"(s) is maximum when a s takes minimum value on [2,10] cs Scanned with CamScanner

. K = f'(S-2) :: K = 3.3757 ETI = (10-2)'s 1. - X 3.375 Tax 42 ? 82 x 3.375 12x16 percentage ... Upper bound for Eyl is g. oliv) Wow we have write g as a e of the integral's true value. . % etter true -9 || true value - X 100 Scanned with CamScanner

:: 15.6-94 x 100 - 3.6 - 5.4 3.5 X 100 = 1:5 X100 = 150% a g is 150% of the integral's true value Scanned with CamScanner