Question

Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for the given value of n. Round your answer to four decimal places and compare the results with the exact value of the definite integral. foxt dx, n = 4 (x + 2)2 Trapezoidal Simpson's exact

Answer 1

an) Griven that dy (X+292 DAY 이= be * Y=fx)= Ax= (X) +Ax) 1 01 1 = 아을 2, 놀 (42) 편 어음해 어른 * 13 아름에 21 육 0.395 2 193 4·32 2 4 (GS) 키 2. ur ot% 1 3 02641 (t = 0 2 22 (+) Trepizoidal rule (c) - 22 12 ((Yot 4,44) + 2(+4ys)) 글 (Costorn} + { c.375 to 31 + 0.14 6M) (12.6g) So we have dy ㅕ101335125 Simpson rule : woke - (41) 444,913) >()) (o sun11)+ulu45 -0.2cm) ->tersa) 0,71221 + 2.4326 + or qu) 。 rim = o(X2)) 0320 33,

Exact value 2. dy do 요 (xt- 2. dus dy 여 al' 잉름 (1) * (월) 해 a where y=x+2 7 - (L) ㅋ (-) · 3333 Trepizoidal rule of Simpson rule - 00331125 013) 0 63 Exay valu 0.33 에 미a - d18 placement given Vt) = --132 213 displaument S (2_t_132d- 13 기 132ㅏ 3 C 2... 133 T (3) 13)(13) - + 4 131 3 134 it displacement 132 distanu 12. 라세32 Bt-132 t12) Alt-1) * (1) (t-12) 3 0 t=-1} Et - 121

dis Pano iSA II ketu) of+ | Overv 아 여 13. 13라 2 가 1-447. 833 | +1.33) ㅜ 997. 833 + 1,633 distane ㅕ 959.666 Sxndxa ) 께