Алгоритм решения БДЗ / 10c

I = ∫1

n

2 x sin x dx;

∑

S(h) = h i=1 f (xi) (ф-ла правых прямоуг.);

h1 = 1=5; h2 = 1=12:

S(0:2) = 0:2(1:1184 + 1:3796 + 1:5993 + 1:7529 + 1:8186) = 1:5338,

S(0:0833) = 0:0833(0:9572 + 1:0727 + 1:1862 + 1:2959 + 1:3999 + 1:4962 + 1:5832 + 1:6590 + 1:7220 + 1:7705 +

1:8032 + 1:8186) = 1:4804,

2

1:4804 1:5338

"Рунге

=

(0:2=0:0833)

2 1

= 0:0112, "практич. = 0:04

I = ∫1

3

n

x3 ln x dx;

h

∑

S(h) =

2

i=1 (f (xi 1) + f (xi)) (ф-ла трапеций);

h1 = 2=6; h2 = 2=10:

S(0:3333) = 0:3333(0:6819 + 2:3649 + 5:5452 + 10:7638 + 18:5994 + 29:6625) = 22:5393,

S(0:2) = 0:2(0:3151 + 0:9233 + 1:9251 + 3:4280 + 5:5452 + 8:3955 + 12:1025 + 16:7941 + 22:6022 + 29:6625) =

20:3387,

3

20:3387 22:5393

"Рунге

=

(0:3333=0:2)2 1

= 1:2378, "практич. = 3:0918

I = ∫1

n

3 sin x sh x dx;

∑

S(h) = h i=1 f (xi 1) (ф-ла левых прямоуг.);

h1 = 2=6; h2 = 2=14:

S(0:3333) = 0:3333(1:7155 + 2:5411 + 3:2979 + 3:6933 + 3:2746 + 1:4137) = 5:3120,

S(0:1429) = 0:1429(1:2814 + 1:6030 + 1:9467 + 2:3029 + 2:6587 + 2:9974 + 3:2979 + 3:5340 + 3:6742 + 3:6809 +

3:5107 + 3:1139 + 2:4351 + 1:4137) = 5:3501,

4

5:3501 5:3120

"Рунге

=

(0:3333=0:1429)2 1

= 0:0086, "практич. = 0:0127

I = ∫1

n

3 sin x sh x dx;

∑

S(h) = h i=1 f (xi) (ф-ла правых прямоуг.);

h1 = 2=4; h2 = 2=10:

S(0:5) = 0:5(2:1239 + 3:2979 + 3:6209 + 1:4137) = 5:2282,

S(0:2) = 0:2(1:4069 + 1:8766 + 2:3746 + 2:8652 + 3:2979 + 3:6036 + 3:6922 + 3:4511 + 2:7442 + 1:4137) = 5:3452,

5

:3452 5:2282

"Рунге

=

5(0:5=0:2)2 1

= 0:0223, "практич. = 0:0078

3

n

1 cos x ch x dx;

∑

h1 = 4=6; h2 = 4=10:

I = ∫

S(h) = h i=1 f (xi 1) (ф-ла левых прямоуг.);

S(0:6667) = 0:6667(0:9979 + 0:9979 + 0:8337 + 0:2624 + 3:5951 + 9:9669) = 7:3299,

S(0:4) = 0:4(0:9784 + 0:9997 + 0:9997 + 0:9784 + 0:8337 + 0:3656 + 0:7060 + 2:6882 + 5:8003 + 9:9669) =

5:6023,

5:6023

7:3299

"Рунге

=

(0:6667=0:4)2 1

= 0:9718, "практич. = 2:3206

3

n

∑

h1 = 4=4; h2 = 4=10:

I = ∫

1 cos x ch x dx; S(h) = h i=1 f (xi) (ф-ла правых прямоуг.);

S(1) = 1(1:0000 + 0:8337 + 1:5656 + 9:9669) = 9:6988,

S(0:4) = 0:4(0:9784 + 0:9997 + 0:9997 + 0:9784 + 0:8337 + 0:3656 + 0:7060 + 2:6882 + 5:8003 + 9:9669) =

5:6023,

7

"

Рунге

=

5:6023

2 9:6988

= 0:7803, "практич. = 2:3206

(1=0:4) 1

I = ∫1

n

∑

3 sin x sh x dx; S(h) = h i=1 f (xi 1) (ф-ла левых прямоуг.);

h1 = 2=6; h2 = 2=14:

S(0:3333) = 0:3333(1:7155 + 2:5411 + 3:2979 + 3:6933 + 3:2746 + 1:4137) = 5:3120,

S(0:1429) = 0:1429(1:2814 + 1:6030 + 1:9467 + 2:3029 + 2:6587 + 2:9974 + 3:2979 + 3:5340 + 3:6742 + 3:6809 +

3:5107 + 3:1139 + 2:4351 + 1:4137) = 5:3501,

8

5:3501 5:3120

"Рунге

=

(0:3333=0:1429)2 1

= 0:0086, "практич. = 0:0127

3

n

∑

h1 = 4=4; h2 = 4=10:

I = ∫

1 cos x ch x dx; S(h) = h i=1 f (xi) (ф-ла правых прямоуг.);

S(1) = 1(1:0000 + 0:8337 + 1:5656 + 9:9669) = 9:6988,

S(0:4) = 0:4(0:9784 + 0:9997 + 0:9997 + 0:9784 + 0:8337 + 0:3656 + 0:7060 + 2:6882 + 5:8003 + 9:9669) =

5:6023,

9

"

Рунге

=

5:6023

2 9:6988

= 0:7803, "практич. = 2:3206

(1=0:4) 1

I = ∫1

n

∑

3 sin x sh x dx; S(h) = h i=1 f (xi 1) (ф-ла левых прямоуг.);

h1 = 2=4; h2 = 2=12:

S(0:5) = 0:5(2:1239 + 3:2979 + 3:6209 + 1:4137) = 5:2282,

S(0:1667) = 0:1667(1:3331 + 1:7155 + 2:1239 + 2:5411 + 2:9430 + 3:2979 + 3:5650 + 3:6933 + 3:6209 + 3:2746 +

2:5703 + 1:4137) = 5:3487,

10

5:3487 5:2282

"Рунге

=

(0:5=0:1667)2 1

= 0:0151, "практич. = 0:0113

I = ∫1

n

∑

3 x3 ln x dx; S(h) = h i=1 f (xi) (ф-ла правых прямоуг.);

h1 = 2=6; h2 = 2=10:

S(0:3333) = 0:3333(0:6819 + 2:3649 + 5:5452 + 10:7638 + 18:5994 + 29:6625) = 22:5393,

S(0:2) = 0:2(0:3151 + 0:9233 + 1:9251 + 3:4280 + 5:5452 + 8:3955 + 12:1025 + 16:7941 + 22:6022 + 29:6625) =

20:3387,

20:3387 22:5393

"Рунге

=

= 1:2378, "практич. = 3:0918

(0:3333=0:2)2 1

I = ∫1

n

3 x3 ln x dx;

∑

S(h) = h i=1 f (xi 1=2) (ф-ла центр. прямоуг.);

h1 = 2=4; h2 = 2=10:

S(0:5) = 0:5(1:3684 + 5:5452 + 14:3170 + 29:6625) = 25:4466,

S(0:2) = 0:2(0:3151 + 0:9233 + 1:9251 + 3:4280 + 5:5452 + 8:3955 + 12:1025 + 16:7941 + 22:6022 + 29:6625) =

20:3387,

12

:3387 25:4466

"Рунге

=

20(0:5=0:2)2 1

= 0:9729, "практич. = 3:0918

4

n

I = ∫3

x2 cos x dx;

h

∑

S(h) =

2

i=1 (f (xi 1) + f (xi)) (ф-ла трапеций);

h1 = 1=5; h2 = 1=12:

I = ∫1

n

∑

2 x sin x dx; S(h) = h i=1 f (xi 1=2) (ô-ëà центр. прямоуг.); h1 = 1=4; h2 = 1=12:

I = ∫1

n

2 x sin x dx;

∑

S(h) = h i=1 f (xi 1) (ф-ла левых прямоуг.);

h1 = 1=6; h2 = 1=10:

S(0:1667) = 0:1667(1:0727 + 1:2959 + 1:4962 + 1:6590 + 1:7705 + 1:8186) = 1:5188,

S(0:1) = 0:1(0:9803 + 1:1184 + 1:2526 + 1:3796 + 1:4962 + 1:5993 + 1:6858 + 1:7529 + 1:7980 + 1:8186) = 1:4882,

15

1:4882 1:5188

"Рунге

=

(0:1667=0:1)2 1

= 0:0172, "практич. = 0:0478

3

n

I = ∫

1 cos x ch x dx;

S(h) = h i=1 f (xi 1) (ф-ла левых прямоуг.);

h1 = 4=8; h2 = 4=12:

∑

3

n

1 cos x ch x dx;

∑

h1 = 4=4; h2 = 4=10:

I = ∫

S(h) = h i=1 f (xi 1=2) (ф-ла центр. прямоуг.);

S(1) = 1(1:0000 + 0:8337 + 1:5656 + 9:9669) = 9:6988,

S(0:4) = 0:4(0:9784 + 0:9997 + 0:9997 + 0:9784 + 0:8337 + 0:3656 + 0:7060 + 2:6882 + 5:8003 + 9:9669) =

5:6023,

17

"

Рунге

=

5:6023 2 9:6988

= 0:7803, "практич. = 2:3206

(1=0:4) 1

I = ∫1

n

3 sin x sh x dx;

∑

S(h) = h i=1 f (xi) (ф-ла правых прямоуг.);

h1 = 2=6; h2 = 2=10:

S(0:3333) = 0:3333(1:7155 + 2:5411 + 3:2979 + 3:6933 + 3:2746 + 1:4137) = 5:3120,

S(0:2) = 0:2(1:4069 + 1:8766 + 2:3746 + 2:8652 + 3:2979 + 3:6036 + 3:6922 + 3:4511 + 2:7442 + 1:4137) = 5:3452,

18

5:3452 5:3120

"Рунге

=

(0:3333=0:2)2 1

= 0:0187, "практич. = 0:0078

I = ∫1

n

3 sin x sh x dx;

∑

S(h) = h i=1 f (xi 1) (ф-ла левых прямоуг.);

h1 = 2=6; h2 = 2=10:

S(0:3333) = 0:3333(1:7155 + 2:5411 + 3:2979 + 3:6933 + 3:2746 + 1:4137) = 5:3120,

S(0:2) = 0:2(1:4069 + 1:8766 + 2:3746 + 2:8652 + 3:2979 + 3:6036 + 3:6922 + 3:4511 + 2:7442 + 1:4137) = 5:3452,

19

5:3452 5:3120

"Рунге

=

(0:3333=0:2)2 1

= 0:0187, "практич. = 0:0078

3

n

1 cos x ch x dx;

∑

h1 = 4=8; h2 = 4=12:

I = ∫

S(h) = h i=1 f (xi) (ф-ла правых прямоуг.);