船舶原理梯形法和辛普森第一法則例題

1、例例題題1 1：分分別別用用5 5個(gè)個(gè)縱縱坐坐標(biāo)標(biāo)值值的的梯梯形形法法、辛辛浦浦生生第第一一法法和和乞乞貝貝雪雪夫夫法法計(jì)計(jì)算算函函數(shù)數(shù)y=tan(x)y=tan(x)從從x=0 x=0到到x x/3/3，的的數(shù)數(shù)值值積積分分值值，并并與與精精確確解解進(jìn)進(jìn)行行比比較較。解解：先先畫(huà)畫(huà)出出y=tan(x)y=tan(x)，從從x=0 x=0到到x=/3x=/3的的圖圖形形，如如圖圖所所示示，其其中中L=/3L=/3，lL/4=/12L/4=/12。（1 1）精精確確解解（2 2）梯梯形形法法坐標(biāo)號(hào)橫坐標(biāo)x縱坐標(biāo)y梯形系數(shù)T.M.面積函數(shù)0000.501/120.2679510.267952/60

2、.5773510.577353/41114/31.732050.50.866032.71133（3 3）辛辛浦浦生生第第一一法法坐標(biāo)號(hào)橫坐標(biāo)x縱坐標(biāo)y辛氏乘數(shù)S.M.面積函數(shù)000101/120.2679541.07182/60.5773521.15473/41444/31.7320511.732057.95855ppp2 2 1 0 7. 09 5 8 5 5. 71 231)424(3)tan(4321030=+=yyyyyld xxAppp2 2 5 9 4. 07 1 1 3 3. 21 2)22()tan(4321030=+=yyyyyld xxAppp2 2 0 6 4. 0c o

3、 sln)ta n(3030=-=xd xxA（4 4）乞乞貝貝雪雪夫夫法法坐標(biāo)號(hào)橫坐標(biāo)x縱坐標(biāo)y乞氏乘數(shù)C.M.面積函數(shù)000.0879310.087931/6-0.8325*/60.1675*/60.3397210.339722/6-0.37454*/60.62546*/60.5773510.577353/60.8765510.876554/6+0.37454*/61.37454*/61.4268211.42682/6+0.8325*/61.8325*/63.30837例例題題2 2：某某船船在在吃吃水水d d4.2m4.2m時(shí)時(shí)的的水水線(xiàn)線(xiàn)分分為為1010等等分分，等等分分間間距距為為l

4、3.5m3.5m，自自船船首首向向船船尾尾的的半半寬寬值值分分別別為為：0 0、3.33.3、5.35.3、5.95.9、5.95.9、5.95.9、5.95.9、5.855.85、5.225.22、3.663.66、1.031.03，用用梯梯形形法法和和辛辛浦浦生生一一法法計(jì)計(jì)算算船船在在此此吃吃水水時(shí)時(shí)的的水水線(xiàn)線(xiàn)面面面面積積。梯梯形形法法坐標(biāo)號(hào)縱坐標(biāo)（1）梯形積分系數(shù)（2）乘積（1）（2）100.5023.313.335.315.345.915.955.915.965.915.975.915.985.8515.8595.2215.22103.6613.66111.030.50.51547

5、.445ppp22056. 030837. 315)(5)tan(4321030=+=yyyyyldxxAppp2 2 1 0 7. 09 5 8 5 5. 71 231)424(3)tan(4321030=+=yyyyyld xxAA=2*3.5*47.445=332.12A=2*3.5*47.445=332.12辛辛浦浦生生一一法法坐標(biāo)號(hào)縱坐標(biāo)（1）辛氏積分系數(shù)（2）乘積（1）（2）101023.3413.235.3210.645.9423.655.9211.865.9423.675.9211.885.85423.495.22210.44103.66414.64111.0311.03144

6、.11A=2*(1/3)*3.5*144.11=336.26A=2*(1/3)*3.5*144.11=336.26例例題題3 3：下下面面是是2600026000噸噸成成品品油油船船在在設(shè)設(shè)計(jì)計(jì)吃吃水水d d9.5m9.5m處處的的一一條條水水線(xiàn)線(xiàn)，試試用用梯梯形形法法和和辛辛浦浦生生一一法法計(jì)計(jì)算算該該水水線(xiàn)線(xiàn)面面的的面面積積。( (注注：原原圖圖形形等等比比例例縮縮小小1010倍倍) )梯梯形形法法站號(hào)縱坐標(biāo)（1）辛氏積分系數(shù)（2）乘積（1）（2）027800.51390172601726021030011030031220011220041324011324051366011366061

7、3700113700713700113700813700113700913700113700101370011370011137001137001213700113700131370011370014137001137001513700113700161350011350017126901126901810820110820197260172602000.502393200 0站站以以后后部部分分的的水水線(xiàn)線(xiàn)面面面面積積A1=20.53830(450+2780)=12370900mmA1=20.53830(450+2780)=12370900mm2 20 0站站到到2020站站的的水水線(xiàn)線(xiàn)面面

8、面面積積A2=2lyiA2=2lyi28200239320282002393203924848000mm3924848000mm2 2整整個(gè)個(gè)水水線(xiàn)線(xiàn)面面面面積積AwAwA1+A2=3937218900mmA1+A2=3937218900mm2 23937.22m3937.22m2 2辛辛浦浦生生一一法法站號(hào)縱坐標(biāo)（1）梯形積分系數(shù)（2）乘積（1）（2）027800.5139017260214520210300110300312200224400413240113240513660227320613700113700713700227400813700113700913700227400101

9、3700113700111370022740012137001137001313700227400141370011370015137002274001613500113500171269022538018108201108201972602145202000.503608900 0站站以以后后部部分分的的水水線(xiàn)線(xiàn)面面面面積積A1=20.53830(450+2780)=12370900mmA1=20.53830(450+2780)=12370900mm2 20 0站站到到2020站站的的水水線(xiàn)線(xiàn)面面面面積積A2=22/3lyiA2=22/3lyi22/3820036089022/3820036

10、08903945730667mm3945730667mm2 2整整個(gè)個(gè)水水線(xiàn)線(xiàn)面面面面積積AwAwA1+A2=3958101567mmA1+A2=3958101567mm2 23958.1m3958.1m2 2例例題題1 1：分分別別用用5 5個(gè)個(gè)縱縱坐坐標(biāo)標(biāo)值值的的梯梯形形法法、辛辛浦浦生生第第一一法法和和乞乞貝貝雪雪夫夫法法計(jì)計(jì)算算函函數(shù)數(shù)y=tan(x)y=tan(x)從從x=0 x=0到到x x/3/3，的的數(shù)數(shù)值值積積分分值值，并并與與精精確確解解進(jìn)進(jìn)行行比比較較。解解：先先畫(huà)畫(huà)出出y=tan(x)y=tan(x)，從從x=0 x=0到到x=/3x=/3的的圖圖形形，如如圖圖所所示示

11、，其其中中L=/3L=/3，lL/4=/12L/4=/12。例例題題2 2：某某船船在在吃吃水水d d4.2m4.2m時(shí)時(shí)的的水水線(xiàn)線(xiàn)分分為為1010等等分分，等等分分間間距距為為l3.5m3.5m，自自船船首首向向船船尾尾的的半半寬寬值值分分別別為為：0 0、3.33.3、5.35.3、5.95.9、5.95.9、5.95.9、5.95.9、5.855.85、5.225.22、3.663.66、1.031.03，用用梯梯形形法法和和辛辛浦浦生生一一法法計(jì)計(jì)算算船船在在此此吃吃水水時(shí)時(shí)的的水水線(xiàn)線(xiàn)面面面面積積。例例題題3 3：下下面面是是2600026000噸噸成成品品油油船船在在設(shè)設(shè)計(jì)計(jì)吃吃

12、水水d d9.5m9.5m處處的的一一條條水水線(xiàn)線(xiàn)，試試用用梯梯形形法法和和辛辛浦浦生生一一法法計(jì)計(jì)算算該該水水線(xiàn)線(xiàn)面面的的面面積積。( (注注：原原圖圖形形等等比比例例縮縮小小1010倍倍) )0 0站站以以后后部部分分的的水水線(xiàn)線(xiàn)面面面面積積A1=20.53830(450+2780)=12370900mmA1=20.53830(450+2780)=12370900mm2 20 0站站到到2020站站的的水水線(xiàn)線(xiàn)面面面面積積A2=2lyiA2=2lyi28200239320282002393203924848000mm3924848000mm2 2整整個(gè)個(gè)水水線(xiàn)線(xiàn)面面面面積積AwAwA1+A2=3937218900mmA1+A2=3937218900mm2 23937.22m3937.22m2 20 0站站以以后后部部分分的的水水線(xiàn)線(xiàn)面面面面積積A1=20.53830(450+2780)=12370900mmA1=20.53830(4