Question

Q7 Integral 15 Points Estimate the error from the trapezoidal rule and Simpson's rule when finding an approximation o lo vædx with 4 equally spaced subintervals of (0,1). to

Answer 1

Solution:

Given that:- {'re With y equally spaced subintervals of Co,] S Voc doc ㅍ here, a-0 b. n-4 fox) = 5x is given by, * Now, the Error due to trapezoidal rule 'Eylk Mq Cb-aj3. Ten2 where Mq = Maximum value of If "(x) l in the interval (ool) i foc). Voc f'(x) = a u f"cx) • _*(J3312 that is, f"C) ::f"(0);- 480 x 3/2 Чxo f"01. si 4x) a -1

leal ýx ci-oja 12x64)2 => -114 12x16 . 768 >> F0.0013 I Egl * Again, the error due to simpson's rule is given by, < M4 cb-ass 18074 Where My = Max value of In caso in the interval Co.] *;' fcat: 150 fo). at 30 f") = 1 1 1 3/2 of") 3 8 x512 fill(x) -15 160412 f"co). -15 1bxo filli (1) -15 16x) -) -15 16

Therefore, My 여혀 (5 16 IEI - 15/13 Cl-005 180 x Cu)4 5 16 186 256 12 49152 -0.00002