T o ‘g ‘ri to ‘rtburchak usulida y o ‘l qo‘y ilg an xatolik quyidagicha aniqlanadi:
\ l - S \ < M h ( b - a ) , M = max^f ( z ^ , z e [ a ; b ] .
1
f a
M iso l. J-------- integralni to ‘g ‘ri to 'rtb u rc h a k usulida
taqribiy hisoblang v a
о
1
+
x
natijani
u n in g aniq q iy m ati arctgX = — » 0,785 bilan taqqoslang.
4
Y ech ish . A n iq lik uchun w = 1 0,
Ax = 0,1 va
x t = £ 0 ,1
(k = 0,1,2,...,10) deb
olib, integral ostidagi
fun k siy a qiym atini
0 ,0 0 1
an iq lik d a hisoblaym iz:
Л = 1. > . = -------— г й 0,9 9 0 ,
> , = ------ -—
т и 0 ,9 6 2 ,
\ + ( 0 , \ ) 2
* 2
\ + ( 0 , 2 ) 2
У> = l + f0 3 / ” 0’917’
^ * 0'862’
^ = ° ' 800>
>.*0,735,
у, *0,671,
y s * 0 ,6 1 0 ,
> - ,» 0 ,5 5 2 , > -,„= 0 ,5 0 0 .
U h o ld a berilgan
integral uchun
S = 0,1 ■
(I + 0,990 + 0,962 + 0,917 + 0,862 + 0,800 + 0,735 +
+ 0,671 + 0,610 + 0,552J я 0,810
Q = 0,1 ■
(0 ,9 9 0 + 0,962 + 0,917 + 0,862 + 0,800 + 0,735 + 0,671 +
+ 0,610 + 0,552 + 0,500
) * 0,755
taqribiy q iy m atlarg a eg a boMamiz, y a ’ni 0 ,7 5 5 < 0 ,7 8 5 < 0 ,8 10. Bu y erd a integralni
taqribiy h iso b lash d a y o ‘l q o ‘yiIgan absolyut xato | / - 5 1< 0,028 dan oshm asligini
0 ,0 2 8 -1 0 0
v a nisbiy xato e s a --------------- « 3,6% ga ten elig in i k o ’rish im iz m um kin.
0,782
5
5 5
A niq integralni to ‘g ‘ri to ‘rtburchak u su lid a taqribiy
hisoblash uchun Paskal
tilid a tu zilg an d astu r m atni: