Question

1 Evaluate (x2 + cos y) dx dy by rectangle rule, tripezoidal rule and Simpson's rule with n= 5 in both directions. - 0 2

Answer 1

Sot": - Guren integral pa 2 - 1 Sexe Gystal Cet 4 2. I Gertasy) de cet f (x) = { retasy), 26[24] Considering the partition, P,= {2, 122, 12 / , 16 , 46 43

2 +2 + [324+G(7 25 74 > 144 95% of 2,41 for mosi with n=1473) - ( ) - by simpson's rule, 1 = Set Cy) dk 1/4(2) + ${4)+2&49)+447) +43x4-4131 = (B)(4+6°) +(167 68) - (22/6/ + 6y + 93760913 is het + Going + B C + oy}] CS) Gy +(62858 *) (Cory to A by Trapezrical Rule, Too Sºx Gyda xn [fe(9)+4,64) +24(23) + f(*)th($)+464) W[(4+6y) +66+607) tay Ront 5 X5 2 256 +2 + 196 25 { tlog 2 + 324 25 + 6149) + Coy + coy} (3) ('ő, co] + C) Goly) + 736) 368 =

314 35 ” 0 Again, considering the functions to(4) year) (cy + * bs (4) – (4 67 + 7 ) YE [11] Crysidering the partition P₂ - {0, + 3 3 4 1} of [1] for n=5, with n= ). then by simpson's rule Steady -41)[4.67+tz(+2{k (6)+fa(} +4454477243}] = { a n = 53.266+ 2{55.398 + 54.141) +4355.728 + 54.862 1.86237 = 154.11 Cupto adecimal places) s '(276(99)dx dy ~ 154.11 (thy!) [by 0) by Trapezoidal sule, Stoc Day -- (4)[$(6)+ t2 (1)+ 2{+)+ 64? + b ()+ 63 ()} 836 1 ice 2 + 31.601+2733. 360 + 33.124 + 32.741 7 32.227 ~ 65.589 le ! ! **+ Gg y) dx dy ~ 65.59 (by ) Cupt 2 decimal places) -3