1). Formula:
|
n=15
|
|||
|
i
|
h
|
x
|
f(x)
|
|
0
|
0.2
|
2
|
2.160685
|
|
1
|
0.2
|
2.2
|
1.396897
|
|
2
|
0.2
|
2.4
|
-0.46354
|
|
3
|
0.2
|
2.6
|
-2.492
|
|
4
|
0.2
|
2.8
|
-3.38849
|
|
5
|
0.2
|
3
|
-2.16469
|
|
6
|
0.2
|
3.2
|
1.102863
|
|
7
|
0.2
|
3.4
|
4.88988
|
|
8
|
0.2
|
3.6
|
6.637013
|
|
9
|
0.2
|
3.8
|
4.076955
|
|
10
|
0.2
|
4
|
-2.96965
|
|
11
|
0.2
|
4.2
|
-11.3601
|
|
12
|
0.2
|
4.4
|
-15.1856
|
|
13
|
0.2
|
4.6
|
-8.75841
|
|
14
|
0.2
|
4.8
|
8.771034
|
|
15
|
0.2
|
5
|
29.74698
|
|
integral
|
-1.14885
|
|
n=18
|
|||
|
i
|
h
|
x
|
f(x)
|
|
0
|
0.166667
|
2
|
2.160685
|
|
1
|
0.166667
|
2.166667
|
1.615642
|
|
2
|
0.166667
|
2.333333
|
0.233824
|
|
3
|
0.166667
|
2.5
|
-1.53607
|
|
4
|
0.166667
|
2.666667
|
-2.97954
|
|
5
|
0.166667
|
2.833333
|
-3.34643
|
|
6
|
0.166667
|
3
|
-2.16469
|
|
7
|
0.166667
|
3.166667
|
0.463566
|
|
8
|
0.166667
|
3.333333
|
3.717558
|
|
9
|
0.166667
|
3.5
|
6.187727
|
|
10
|
0.166667
|
3.666667
|
6.3309
|
|
11
|
0.166667
|
3.833333
|
3.173182
|
|
12
|
0.166667
|
4
|
-2.96965
|
|
13
|
0.166667
|
4.166667
|
-10.0998
|
|
14
|
0.166667
|
4.333333
|
-14.8212
|
|
15
|
0.166667
|
4.5
|
-13.4761
|
|
16
|
0.166667
|
4.666667
|
-3.96421
|
|
17
|
0.166667
|
4.833333
|
12.36963
|
|
18
|
0.166667
|
5
|
29.74698
|
|
integral
|
-1.12067
|
|
n=21
|
|||
|
i
|
h
|
x
|
f(x)
|
|
0
|
0.142857
|
2
|
2.160685
|
|
1
|
0.142857
|
2.142857
|
1.750768
|
|
2
|
0.142857
|
2.285714
|
0.694221
|
|
3
|
0.142857
|
2.428571
|
-0.77191
|
|
4
|
0.142857
|
2.571429
|
-2.24088
|
|
5
|
0.142857
|
2.714286
|
-3.22291
|
|
6
|
0.142857
|
2.857143
|
-3.27741
|
|
7
|
0.142857
|
3
|
-2.16469
|
|
8
|
0.142857
|
3.142857
|
0.022949
|
|
9
|
0.142857
|
3.285714
|
2.798551
|
|
10
|
0.142857
|
3.428571
|
5.328483
|
|
11
|
0.142857
|
3.571429
|
6.612512
|
|
12
|
0.142857
|
3.714286
|
5.781207
|
|
13
|
0.142857
|
3.857143
|
2.450493
|
|
14
|
0.142857
|
4
|
-2.96965
|
|
15
|
0.142857
|
4.142857
|
-9.1395
|
|
16
|
0.142857
|
4.285714
|
-13.9431
|
|
17
|
0.142857
|
4.428571
|
-14.9898
|
|
18
|
0.142857
|
4.571429
|
-10.4179
|
|
19
|
0.142857
|
4.714286
|
0.174963
|
|
20
|
0.142857
|
4.857143
|
14.97701
|
|
21
|
0.142857
|
5
|
29.74698
|
|
integral
|
-1.10922
|
|
n=24
|
|||
|
i
|
h
|
x
|
f(x)
|
|
0
|
0.125
|
2
|
2.160685
|
|
1
|
0.125
|
2.125
|
1.840052
|
|
2
|
0.125
|
2.25
|
1.009355
|
|
3
|
0.125
|
2.375
|
-0.19698
|
|
4
|
0.125
|
2.5
|
-1.53607
|
|
5
|
0.125
|
2.625
|
-2.6925
|
|
6
|
0.125
|
2.75
|
-3.33745
|
|
7
|
0.125
|
2.875
|
-3.20388
|
|
8
|
0.125
|
3
|
-2.16469
|
|
9
|
0.125
|
3.125
|
-0.29643
|
|
10
|
0.125
|
3.25
|
2.090416
|
|
11
|
0.125
|
3.375
|
4.471373
|
|
12
|
0.125
|
3.5
|
6.187727
|
|
13
|
0.125
|
3.625
|
6.583558
|
|
14
|
0.125
|
3.75
|
5.182271
|
|
15
|
0.125
|
3.875
|
1.868728
|
|
16
|
0.125
|
4
|
-2.96965
|
|
17
|
0.125
|
4.125
|
-8.39421
|
|
18
|
0.125
|
4.25
|
-13.0031
|
|
19
|
0.125
|
4.375
|
-15.178
|
|
20
|
0.125
|
4.5
|
-13.4761
|
|
21
|
0.125
|
4.625
|
-7.10767
|
|
22
|
0.125
|
4.75
|
3.606537
|
|
23
|
0.125
|
4.875
|
16.93618
|
|
24
|
0.125
|
5
|
29.74698
|
|
integral
|
-1.10385
|
ROMBERG’S INTEGRATION
|
-1.148851445
|
-1.120665894
|
-1.109218915
|
-1.103848716
|
|||||
|
n=1
|
-1.158246629
|
-1.124481554
|
-1.111008981
|
|||||
|
n=2
|
-1.160497634
|
-1.125379726
|
||||||
|
n=3
|
-1.161055061
|
|||||||
2). Solve the bigger
area that is bounded by a parabola, 
and a circle, 
Use n=10, n=14, n =18,
n=22. Then solve the improved area using Romberg’s Integration.
and a circle, Use n=10, n=14, n =18,
n=22. Then solve the improved area using Romberg’s Integration.|
x+
|
0.675445
|
y+
|
7.159113
|
|
|
x-
|
-0.67544
|
y-
|
7.764638
|
|
delta y
|
-0.60553
|
||||
|
n
|
10
|
||||
|
k
|
delta y
|
yk
|
xr - p
|
xl - l
|
xk
|
|
0
|
-0.06055
|
7.764638
|
-0.67544
|
8.646673
|
-9.32212
|
|
1
|
-0.06055
|
7.704086
|
-0.53211
|
8.724457
|
-9.25656
|
|
2
|
-0.06055
|
7.643533
|
-0.3906
|
8.799684
|
-9.19028
|
|
3
|
-0.06055
|
7.582981
|
-0.25093
|
8.872504
|
-9.12343
|
|
4
|
-0.06055
|
7.522428
|
-0.11309
|
8.94305
|
-9.05614
|
|
5
|
-0.06055
|
7.461876
|
0.022916
|
9.011442
|
-8.98853
|
|
6
|
-0.06055
|
7.401323
|
0.157089
|
9.077788
|
-8.9207
|
|
7
|
-0.06055
|
7.340771
|
0.289428
|
9.142187
|
-8.85276
|
|
8
|
-0.06055
|
7.280218
|
0.419933
|
9.204727
|
-8.78479
|
|
9
|
-0.06055
|
7.219666
|
0.548606
|
9.265492
|
-8.71689
|
|
10
|
-0.06055
|
7.159113
|
0.675445
|
9.324555
|
-8.64911
|
|
area
|
5.442201
|
|
n
|
14
|
||||
|
k
|
delta y
|
yk
|
xr - p
|
xl - l
|
xk
|
|
0
|
-0.04325
|
7.764638
|
-0.67544
|
8.646673
|
-9.32212
|
|
1
|
-0.04325
|
7.721387
|
-0.57287
|
8.7025
|
-9.27537
|
|
2
|
-0.04325
|
7.678135
|
-0.47124
|
8.757001
|
-9.22824
|
|
3
|
-0.04325
|
7.634883
|
-0.37053
|
8.810231
|
-9.18077
|
|
4
|
-0.04325
|
7.591631
|
-0.27077
|
8.862243
|
-9.13301
|
|
5
|
-0.04325
|
7.548379
|
-0.17194
|
8.913086
|
-9.08503
|
|
6
|
-0.04325
|
7.505128
|
-0.07404
|
8.962805
|
-9.03685
|
|
7
|
-0.04325
|
7.461876
|
0.022916
|
9.011442
|
-8.98853
|
|
8
|
-0.04325
|
7.418624
|
0.118941
|
9.059035
|
-8.94009
|
|
9
|
-0.04325
|
7.375372
|
0.21403
|
9.10562
|
-8.89159
|
|
10
|
-0.04325
|
7.33212
|
0.308183
|
9.151233
|
-8.84305
|
|
11
|
-0.04325
|
7.288868
|
0.401402
|
9.195904
|
-8.7945
|
|
12
|
-0.04325
|
7.245617
|
0.493685
|
9.239663
|
-8.74598
|
|
13
|
-0.04325
|
7.202365
|
0.585032
|
9.282538
|
-8.69751
|
|
14
|
-0.04325
|
7.159113
|
0.675445
|
9.324555
|
-8.64911
|
|
area
|
5.442207
|
|
n
|
18
|
||||
|
k
|
delta y
|
yk
|
xr - p
|
xl - l
|
Xk
|
|
0
|
-0.03364
|
7.764638
|
-0.67544
|
8.646673
|
-9.32212
|
|
1
|
-0.03364
|
7.730998
|
-0.59559
|
8.690211
|
-9.2858
|
|
2
|
-0.03364
|
7.697358
|
-0.51629
|
8.732939
|
-9.24923
|
|
3
|
-0.03364
|
7.663717
|
-0.43757
|
8.774883
|
-9.21245
|
|
4
|
-0.03364
|
7.630077
|
-0.3594
|
8.816069
|
-9.17547
|
|
5
|
-0.03364
|
7.596437
|
-0.28181
|
8.856523
|
-9.13833
|
|
6
|
-0.03364
|
7.562797
|
-0.20478
|
8.896266
|
-9.10104
|
|
7
|
-0.03364
|
7.529156
|
-0.12831
|
8.93532
|
-9.06363
|
|
8
|
-0.03364
|
7.495516
|
-0.05242
|
8.973706
|
-9.02612
|
|
9
|
-0.03364
|
7.461876
|
0.022916
|
9.011442
|
-8.98853
|
|
10
|
-0.03364
|
7.428235
|
0.097683
|
9.048547
|
-8.95086
|
|
11
|
-0.03364
|
7.394595
|
0.171883
|
9.085038
|
-8.91315
|
|
12
|
-0.03364
|
7.360955
|
0.245518
|
9.120931
|
-8.87541
|
|
13
|
-0.03364
|
7.327315
|
0.318587
|
9.156242
|
-8.83765
|
|
14
|
-0.03364
|
7.293674
|
0.39109
|
9.190986
|
-8.7999
|
|
15
|
-0.03364
|
7.260034
|
0.463028
|
9.225176
|
-8.76215
|
|
16
|
-0.03364
|
7.226394
|
0.534399
|
9.258826
|
-8.72443
|
|
17
|
-0.03364
|
7.192753
|
0.605205
|
9.291948
|
-8.68674
|
|
18
|
-0.03364
|
7.159113
|
0.675445
|
9.324555
|
-8.64911
|
|
area
|
5.44221
|
|
N
|
22
|
||||
|
K
|
delta y
|
yk
|
xr - p
|
xl - l
|
xk
|
|
0
|
-0.02752
|
7.764638
|
-0.67544
|
8.646673
|
-9.32212
|
|
1
|
-0.02752
|
7.737114
|
-0.61006
|
8.682356
|
-9.29242
|
|
2
|
-0.02752
|
7.709591
|
-0.54506
|
8.717493
|
-9.26255
|
|
3
|
-0.02752
|
7.682067
|
-0.48044
|
8.7521
|
-9.23254
|
|
4
|
-0.02752
|
7.654543
|
-0.41619
|
8.786189
|
-9.20238
|
|
5
|
-0.02752
|
7.627019
|
-0.35233
|
8.819777
|
-9.1721
|
|
6
|
-0.02752
|
7.599495
|
-0.28884
|
8.852875
|
-9.14171
|
|
7
|
-0.02752
|
7.571971
|
-0.22573
|
8.885496
|
-9.11123
|
|
8
|
-0.02752
|
7.544447
|
-0.163
|
8.917652
|
-9.08065
|
|
9
|
-0.02752
|
7.516923
|
-0.10065
|
8.949355
|
-9.05
|
|
10
|
-0.02752
|
7.4894
|
-0.03868
|
8.980614
|
-9.01929
|
|
11
|
-0.02752
|
7.461876
|
0.022916
|
9.011442
|
-8.98853
|
|
12
|
-0.02752
|
7.434352
|
0.084131
|
9.041847
|
-8.95772
|
|
13
|
-0.02752
|
7.406828
|
0.144967
|
9.071838
|
-8.92687
|
|
14
|
-0.02752
|
7.379304
|
0.205424
|
9.101426
|
-8.896
|
|
15
|
-0.02752
|
7.35178
|
0.265502
|
9.130619
|
-8.86512
|
|
16
|
-0.02752
|
7.324256
|
0.325202
|
9.159424
|
-8.83422
|
|
17
|
-0.02752
|
7.296732
|
0.384523
|
9.18785
|
-8.80333
|
|
18
|
-0.02752
|
7.269209
|
0.443465
|
9.215905
|
-8.77244
|
|
19
|
-0.02752
|
7.241685
|
0.502028
|
9.243596
|
-8.74157
|
|
20
|
-0.02752
|
7.214161
|
0.560212
|
9.270931
|
-8.71072
|
|
21
|
-0.02752
|
7.186637
|
0.618018
|
9.297915
|
-8.6799
|
|
22
|
-0.02752
|
7.159113
|
0.675445
|
9.324555
|
-8.64911
|
|
AREA
|
5.442211
|
ROMBERG’S INTEGRATION
|
5.442201016
|
5.442207305
|
5.442209894
|
5.442211205
|
||||||
|
N=1
|
5.44219892
|
5.442206442
|
5.442209457
|
||||||
|
n=2
|
5.442198419
|
5.442206241
|
|||||||
|
n=3
|
5.442198294
|
||||||||
Walang komento:
Mag-post ng isang Komento