2024年9月trapezoidalsum（用龙贝格法求积分）

　　⑴trapezoidalsum（用龙贝格法求积分

　　⑵先用另外种方法。formatlong%【】精确值。符号积分it=int(’(/sqrt(pi))*exp(-x)’,,)Aurate=eval(it)y=inline(’(/sqrt(pi))*exp(-x)’)%【】Simpson方法Simpson=quad(y,,)delta=Simpson-Aurate结果：Aurate=.y=Inlinefunction:y(x)=(/sqrt(pi))*exp(-x)Simpson=.delta=.e-【】从网上找到一个，存为romberg.m%=================functionR=romberg(f,a,b,n)formatlong%ROMBERG--puteRombergtableintegralapproximation.%%SYNOPSIS:%R=romberg(f,a,b,n)%%DESCRIPTION:%putesthepleteRombergtableapproximationtotheintegral%%/b%I=|f(x)dx%/a%%PARAMETERS:%f-Theintegrand.Assumedtobeafunctioncallableas%y=f(x)%with`x’in.%a-Leftintegrationintervalendpoint.%b-Rightintegrationintervalendpoint.%n-MaximumlevelinRombergtable.%%RETURNS:%R-Rombergtable.Representedasan(n+)-by-(n+)lower%triangularmatrixofintegralapproximations.%%SEEALSO:%TRAPZ,QUAD,QUADL.%NOTE:allindicesadjustedforMATLAB’sone-basedindexingscheme.%Pre-allocatetheRombergtable.Avoidssubsequentre-allocationwhich%isoftenverycostly.R=zeros();%Initialapproximation.Singleintervaltrapezoidalrule.R(+,+)=(b-a)/*(feval(f,a)+feval(f,b));%FirstcolumnofRombergtable.Increasinglyauratetrapezoidal%approximations.fori=:n,h=(b-a)/^i;s=;fork=:^(i-),s=s+feval(f,a+(*k-)*h);endR(i+,+)=R(i-+,+)/+h*s;end%RichardsonextrapolationgivesremainderofRombergtable.%%Note:Thetableisputedbycolumnsratherthanthemore%traditionalrowversion.Thereasonisthatthispreventsfrequent%(andneedless)re-putationofthe`fac’quantity.%%Moreover,MATLABmatricesinternallyuse``columnmajor’’orderingso%thisversionislessharmfultoputermemorycachesystems.This%reasonisanimplementationaldetail,though,andlessimportantin%introductorycoursessuchasMA.forj=:n,fac=/(^j-);form=j:n,R(m+,j+)=R(m+,j-+)+fac*(R(m+,j-+)-R(m-+,j-+));endendfunctionff=f(x)ff=/sqrt(pi)*exp(-x);%=================运行：》》R=romberg(’f’,,,)R=.....................

　　⑶高等数学arcsin（x分之的定义域是什么

　　⑷点“考研竞赛数学”↑可每天“涨姿势”哦！图片来源：pexels.内容来源：上海外教网V、X、ZValueoffunction：函数值Variable：变数Vector：向量Velocity：速度Verticalasymptote：垂直渐近线Volume：体积X-axis：x轴x-coordinate：x坐标x-intercept：x截距Zerovector：函数的零点Zerosofapolynomial：多项式的零点TTangentfunction：正切函数Tangentline：切线Tangentplane：切平面Tangentvector：切向量Totaldifferential：全微分Trigonometricfunction：三角函数Trigonometricintegrals：三角积分Trigonometricsubstitutions：三角代换法Tripeintegrals：三重积分SSaddlepoint：鞍点Scalar：纯量Secantline：割线Secondderivative：二阶导数SecondDerivativeTest：二阶导数试验法Secondpartialderivative：二阶偏导数Sector：扇形Sequence：数列Series：级数Set：集合Shellmethod：剥壳法Sinefunction：正弦函数Singularity：奇点Slantasymptote：斜渐近线Slope：斜率Slope-interceptequationofaline：直线的斜截式Smoothcurve：平滑曲线Smoothsurface：平滑曲面Solidofrevolution：旋转体Space：空间Speed：速率Sphericalcoordinates：球面坐标SqueezeTheorem：夹挤定理Stepfunction：阶梯函数Strictlydecreasing：严格递减Strictlyincreasing：严格递增Sum：和Surface：曲面Surfaceintegral：面积分Surfaceofrevolution：旋转曲面Symmetry：对称RRadiusofconvergence：收敛半径Rangeofafunction：函数的值域Rateofchange：变化率Rationalfunction：有理函数Rationalizingsubstitution：有理代换法Rationalnumber：有理数Realnumber：实数Rectangularcoordinates：直角坐标Rectangularcoordinatesystem：直角坐标系Relativemaximumandminimum：相对极大值与极小值Revenuefunction：收入函数Revolution,solidof：旋转体Revolution,surfaceof：旋转曲面RiemannSum：黎曼和Riemanniangeometry：黎曼几何Right-handderivative：右导数Right-handlimit：右极限Root：根P、QParabola：抛物线Paraboliylinder：抛物柱面Paraboloid：抛物面Parallelepiped：平行六面体Parallellines：并行线Parameter：参数Partialderivative：偏导数Partialdifferentialequation：偏微分方程Partialfractions：部分分式Partialintegration：部分积分Partiton：分割Period：周期Periodicfunction：周期函数Perpendicularlines：垂直线Piecewisedefinedfunction：分段定义函数Plane：平面Pointofinflection：反曲点Polaraxis：极轴Polarcoordinate：极坐标Polarequation：极方程式Pole：极点Polynomial：多项式Positiveangle：正角Point-slopeform：点斜式Powerfunction：幂函数Product：积Quadrant：象限QuotientLawoflimit：极限的商定律QuotientRule：商定律M、N、OMaximumandminimumvalues：极大与极小值MeanValueTheorem：均值定理Multipleintegrals：重积分Multiplier：乘子Naturalexponentialfunction：自然指数函数Naturallogarithmfunction：自然对数函数Naturalnumber：自然数Normalline：法线Normalvector：法向量Number：数Octant：卦限Oddfunction：奇函数One-sidedlimit：单边极限Openinterval：开区间Optimizationproblems：最佳化问题Order：阶Ordinarydifferentialequation：常微分方程Origin：原点Orthogonal：正交的LLaplacetransform：Leplace变换LawofCosines：余弦定理Leastupperbound：最小上界Left-handderivative：左导数Left-handlimit：左极限Lemniscate：双钮线Length：长度Levelcurve：等高线L’Hospital’srule：洛必达法则Limacon：蚶线Limit：极限Linearapproximation：线性近似Linearequation：线性方程式Linearfunction：线性函数Linearity：线性Linearization：线性化Lineintheplane：平面上之直线Lineinspace：空间之直线Lobachevskigeometry：罗巴切夫斯基几何Localextremum：局部极值Localmaximumandminimum：局部极大值与极小值Logarithm：对数Logarithmicfunction：对数函数IImplicitdifferentiation：隐求导法Implicitfunction：隐函数Improperintegral：瑕积分Increasing/DecreasingTest：递增或递减试验法Increment：增量IncreasingFunction：增函数Indefiniteintegral：不定积分Independentvariable：自变数Indeterminatefrom：不定型Inequality：不等式Infinitepoint：无穷极限Infiniteseries：无穷级数Inflectionpoint：反曲点Instantaneousvelocity：瞬时速度Integer：整数Integral：积分Integrand：被积分式Integration：积分Integrationbypart：分部积分法Intercepts：截距IntermediatevalueofTheorem：中间值定理Interval：区间Inversefunction：反函数Inversetrigonometricfunction：反三角函数Iteratedintegral：逐次积分HHighermathematics高等数学/高数E、F、G、HEllipse：椭圆Ellipsoid：椭圆体Epicycloid：外摆线Equation：方程式Evenfunction：偶函数ExpectedValued：期望值ExponentialFunction：指数函数Exponents,lawsof：指数率Extremevalue：极值ExtremeValueTheorem：极值定理Factorial：阶乘FirstDerivativeTest：一阶导数试验法Firstoctant：第一卦限Focus：焦点Fractions：分式Function：函数FundamentalTheoremofCalculus：微积分基本定理Geometricseries：几何级数Gradient：梯度Graph：图形GreenFormula：格林公式Half-angleformulas：半角公式Harmonicseries：调和级数Helix：螺旋线HigherDerivative：高阶导数Horizontalasymptote：水平渐近线Horizontalline：水平线Hyperbola：双曲线Hyperboloid：双曲面DDecreasingfunction：递减函数Decreasingsequence：递减数列Definiteintegral：定积分Degreeofapolynomial：多项式之次数Density：密度Derivative：导数ofapositefunction：复合函数之导数ofaconstantfunction：常数函数之导数directional：方向导数domainof：导数之定义域ofexponentialfunction：指数函数之导数higher：高阶导数partial：偏导数ofapowerfunction：幂函数之导数ofapowerseries：羃级数之导数ofaproduct：积之导数ofaquotient：商之导数asarateofchange：导数当作变率right-hand：右导数second：二阶导数astheslopeofatangent：导数看成切线之斜率Determinant：行列式Differentiablefunction：可导函数Differential：微分Differentialequation：微分方程partial：偏微分方程Differentiation：求导法implicit：隐求导法partial：偏微分法termbyterm：逐项求导法Directionalderivatives：方向导数Discontinuity：不连续性Diskmethod：圆盘法Distance：距离Divergence：发散Domain：定义域Dotproduct：点积Doubleintegral：二重积分changeofvariablein：二重积分之变数变换inpolarcoordinates：极坐标二重积分alculus：微积分differential：微分学integral：积分学Cartesiancoordinates：笛卡儿坐标一般指直角坐标Cartesiancoordinatessystem：笛卡儿坐标系Cauch’sMeanValueTheorem：柯西均值定理ChainRule：连锁律Changeofvariables：变数变换Circle：圆Circularcylinder：圆柱Closedinterval：封闭区间Coefficient：系数positionoffunction：函数之合成poundinterest：复利Concavity：凹性Conchoid：蚌线Cone：圆锥Constantfunction：常数函数Constantofintegration：积分常数Continuity：连续性atapoint：在一点处之连续性ofafunction：函数之连续性onaninterval：在区间之连续性fromtheleft：左连续fromtheright：右连续Continuousfunction：连续函数Convergence：收敛intervalof：收敛区间radiusof：收敛半径Convergentsequence：收敛数列series：收敛级数Coordinate：s：坐标Cartesian：笛卡儿坐标cylindrical：柱面坐标polar：极坐标rectangular：直角坐标spherical：球面坐标Coordinateaxes：坐标轴Coordinateplanes：坐标平面Cosinefunction：余弦函数Criticalpoint：临界点Cubicfunction：三次函数Curve：曲线Cylinder：圆柱CylindricalCoordinates：圆柱坐标A、BAbsoluteconvergence：绝对收敛Absoluteextremevalues：绝对极值Absolutemaximumandminimum：绝对极大与极小Absolutevalue：绝对值Absolutevaluefunction：绝对值函数Aeleration：加速度Antiderivative：反导数Approximateintegration：近似积分Approximation：逼近法bydifferentials：用微分逼近linear：线性逼近法bySimpson’sRule：Simpson法则逼近法bytheTrapezoidalRule：梯形法则逼近法Arbitraryconstant：任意常数Arclength：弧长Area：面积underacurve：曲线下方之面积betweencurves：曲线间之面积inpolarcoordinates：极坐标表示之面积ofasectorofacircle：扇形之面积ofasurfaceofarevolution：旋转曲面之面积Asymptote：渐近线horizontal：水平渐近线slant：斜渐近线vertical：垂直渐近线Averagespeed：平均速率Averagevelocity：平均速度Axes,coordinate：坐标轴Axesofellipse：椭圆之轴Binomialseries：二项级数

　　⑸翻译，不要用翻译机，翻译好再加分

　　⑹heassociatedthesefactswithcalculus:dyisthedifferentialofthefirstorder,andthesumofthemisy,forinstance,+++=.Leibenizthoughtthattheinvertibilityofdifferenceandsumequalstotheinvertiblityofthesolutionoftangentlineandintegration.theonlydistinctionisthatthedifferenceoftwoelements,belongingtothepascalalgebraicaltriangleandharmonicaltrianglerespectively,isfinite,whilethedifferentialofco-ordinateisinfinitelysmall.thisshowsthathehasalreadyassociatedhisearilerstudyonfinitequantityandtheinvertiblityofdifferentialwiththethoughtonthecalculationofinfinitelysmallquantities.italsocanbeobservedthattheviewofleibenizoncalculusisalgebraical,notgeometrical.tosolvetheproblemofintegration,leibeniznotedyastheareaofcurved-trapezoidalundertheplane-curve.thus,thelongitudinalcoordinateisrelatedtothevariableofarea.fewyearslater,henotedSydxasthearea,inwhich“∫”isthestretchedinitialletterofwordsum.onsolvingtheproblemofdifferential,thatis,differentiation,leibenizintroducednotationx/dtomotethedifferentiationofx,whichmeansreductionofthesameorder.healsothoughtthatiftherearedifferentialofdistinctorder,onlythelowestoneshouldbetaken,andabandonallthehigherorder.astothereason,heprovidedseveralexplanation,however,noneofthemissufficient.actually,heregardedthemethodasanpostulate.lateron,healteredx/dintodx,whichhasbeenadoptedandisusetillnow.绝对亲自翻译，好久不干这个，差点蒙了

　　⑺谁能帮我把下列短文翻译成英文

　　⑻----TheOlympicGamesandthesmallsailingshipworldseriesalladoptstheroutematchthepetitionform.Attendstheidenticalprojectpetitiontheshipunificationtosetsail.Apetitiongenerallycarrieson-turn,eachwheelpetesthefirstminute,thesecondminute,analogizesinturn.Removesoneaftertwoturnsofworstresult,arrangesthefinalpositionaordingtotheeachturnofresultsumofintegral,scorespointsfewfortobesuperior.Eachturnofpetitiongenerallymustcarryonminutestohours.petitionperiod,theemulationboardbasisdailywindpowercondition,arrangestwotothreeturnsofpetitions.UsesthepetitionroutearemanyfortheOlympicstrapezoidalroute,thisroutehascontainedagainstthewind,thecrosswindand尾风therange.Inadditionalsohasthetrianglerouteandthesausageshaperoute.Stemmingfromtothemeteorologyandthesafeconsideration,theemulationboardmayreduceapetitionturnoforderaordingtothewindpowersize.----Thesailingshippetitioninaquaticmeetsafavorableopportunitytohavetocarryoutasetonlandtrafficregulationstobemoreplexthanmanytrafficrules.Theathletewantstowanttoobtaintheresult,mustripelypasspageofthickcontestrules(EnglishtobecalledRRS),pageofthickregularcasesanalysesandapageofaboverankrule.Infrontofthematchalsomuststudyothertworegulartexts--contestrule(NoR)andthenavigationregulation(SIs).Howusestherulesuppressionmatch,causesoneselftomakeaprofitistheimportanttopicwhichtheathleteandthetrainerneedstoconcentrateonstudy.Thesailingshipcontestrulemainlyincludesthetrafficrules,thepetitionimplementationruleandtheprotesttriestostipulatethreemajorparts.ThisruleeveryyearsreviseaftertheOlympicGamesyeartime.Theinternationalsailassociationalsodistributestheruletoexplain,casewhichdistributesincludingeveryyear.Allcasesallareobeythenewestrulerevisiontopileandprint.----Inthetrafficrulesmonlyusedarrivesis--theportesthewindthesailingshiptohavetogivewaytotrafficthestarboardtoethewindtheship;Isintheweathergagetheshiptohavetogivewaytotraffictheleewardship;Whenmeetstheroutebuoyortheobstacle,latterapproachedthisobjecttheshiptohavetogivewaytotrafficalreadyapproachesthisobjecttheship,wasintheflanktheshiptohavetogivewaytotraffictheinsideship.Thepetitionimplementationrulehadmainlystipulatedthepetitionanizationandthemanagementstandard,likesetsailthemethodandthesignalnoticemethodandsoon.Theprotesttriesthestipulationissolvestheathleteinaquatictomeetoneanotherwithbumpshasthedisputeorviolatesaregulationanafterentiresetofrulingmethod.

　　⑼复化梯形求积公式和复化矩形求积公式在求权系数时有啥不同

　　⑽main.mg=(t)exp(-t.^);x=linspace(,,);y=zeros(,);y=zeros(,);fori=:y(i)=/sqrt(pi)*Simpson(g,,x(i),);%幸普森公式y(i)=/sqrt(pi)*trapezoidal(g,,x(i),);%复合梯形公式endplot(x,y,’r-’,x,y,’b.’);legend(’辛普森公式’,’复合梯形公式’);Simpson.mfunctiony=Simpson(f,a,b,M)%f被积函数；a积分下限；b积分上限；M子区间个数（将x分为多少个区间h=(b-a)/(*M);s=;s=;fori=:Mx=a+(*i-)*h;s=s+f(x);endforj=:(M-)x=a+*j*h;s=s+f(x);endy=h/*(f(a)+*s+*s+f(b));endtrapezoidal.mfunctiony=trapezoidal(f,a,b,n)h=(b-a)/n;x=zeros(,n+);F=zeros(,n+);fork=:nx(k+)=a+k*h;ifx(k+)==x(k+)=^(-);endendT_=h/*(f(x())+f(x(n+)));fori=:nF(i)=h*f(x(i));endT_=sum(F);y=T_+T_;end

　　⑾V、X、Z:Valueoffunction：函数值Variable：变数Vector：向量Velocity：速度Verticalasymptote：垂直渐近线Volume：体积X-axis：x轴x-coordinate：x坐标x-intercept：x截距Zerovector：函数的零点Zerosofapolynomial：多项式的零点T:Tangentfunction：正切函数Tangentline：切线Tangentplane：切平面Tangentvector：切向量Totaldifferential：全微分Trigonometricfunction：三角函数Trigonometricintegrals：三角积分Trigonometricsubstitutions：三角代换法Tripeintegrals：三重积分S:Saddlepoint：鞍点Scalar：纯量Secantline：割线Secondderivative：二阶导数SecondDerivativeTest：二阶导数试验法Secondpartialderivative：二阶偏导数Sector：扇形Sequence：数列Series：级数Set：集合Shellmethod：剥壳法Sinefunction：正弦函数Singularity：奇点Slantasymptote：斜渐近线Slope：斜率Slope-interceptequationofaline：直线的斜截式Smoothcurve：平滑曲线Smoothsurface：平滑曲面Solidofrevolution：旋转体Space：空间Speed：速率Sphericalcoordinates：球面坐标SqueezeTheorem：夹挤定理Stepfunction：阶梯函数Strictlydecreasing：严格递减Strictlyincreasing：严格递增Sum：和Surface：曲面Surfaceintegral：面积分Surfaceofrevolution：旋转曲面Symmetry：对称R:Radiusofconvergence：收敛半径Rangeofafunction：函数的值域Rateofchange：变化率Rationalfunction：有理函数Rationalizingsubstitution：有理代换法Rationalnumber：有理数Realnumber：实数Rectangularcoordinates：直角坐标Rectangularcoordinatesystem：直角坐标系Relativemaximumandminimum：相对极大值与极小值Revenuefunction：收入函数Revolution,solidof：旋转体Revolution,surfaceof：旋转曲面RiemannSum：黎曼和Riemanniangeometry：黎曼几何Right-handderivative：右导数Right-handlimit：右极限Root：根P、Q:Parabola：抛物线Paraboliylinder：抛物柱面Paraboloid：抛物面Parallelepiped：平行六面体Parallellines：并行线Parameter：参数Partialderivative：偏导数Partialdifferentialequation：偏微分方程Partialfractions：部分分式Partialintegration：部分积分Partiton：分割Period：周期Periodicfunction：周期函数Perpendicularlines：垂直线Piecewisedefinedfunction：分段定义函数Plane：平面Pointofinflection：反曲点Polaraxis：极轴Polarcoordinate：极坐标Polarequation：极方程式Pole：极点Polynomial：多项式Positiveangle：正角Point-slopeform：点斜式Powerfunction：幂函数Product：积Quadrant：象限QuotientLawoflimit：极限的商定律QuotientRule：商定律M、N、O:Maximumandminimumvalues：极大与极小值MeanValueTheorem：均值定理Multipleintegrals：重积分Multiplier：乘子Naturalexponentialfunction：自然指数函数Naturallogarithmfunction：自然对数函数Naturalnumber：自然数Normalline：法线Normalvector：法向量Number：数Octant：卦限Oddfunction：奇函数One-sidedlimit：单边极限Openinterval：开区间Optimizationproblems：最佳化问题Order：阶Ordinarydifferentialequation：常微分方程Origin：原点Orthogonal：正交的L:Laplacetransform：Leplace变换LawofCosines：余弦定理Leastupperbound：最小上界Left-handderivative：左导数Left-handlimit：左极限Lemniscate：双钮线Length：长度Levelcurve：等高线L’Hospital’srule：洛必达法则Limacon：蚶线Limit：极限Linearapproximation：线性近似Linearequation：线性方程式Linearfunction：线性函数Linearity：线性Linearization：线性化Lineintheplane：平面上之直线Lineinspace：空间之直线Lobachevskigeometry：罗巴切夫斯基几何Localextremum：局部极值Localmaximumandminimum：局部极大值与极小值Logarithm：对数Logarithmicfunction：对数函数I:Implicitdifferentiation：隐求导法Implicitfunction：隐函数Improperintegral：瑕积分Increasing/DecreasingTest：递增或递减试验法Increment：增量IncreasingFunction：增函数Indefiniteintegral：不定积分Independentvariable：自变数Indeterminatefrom：不定型Inequality：不等式Infinitepoint：无穷极限Infiniteseries：无穷级数Inflectionpoint：反曲点Instantaneousvelocity：瞬时速度Integer：整数Integral：积分Integrand：被积分式Integration：积分Integrationbypart：分部积分法Intercepts：截距IntermediatevalueofTheorem：中间值定理Interval：区间Inversefunction：反函数Inversetrigonometricfunction：反三角函数Iteratedintegral：逐次积分H:Highermathematics高等数学/高数E、F、G、H:Ellipse：椭圆Ellipsoid：椭圆体Epicycloid：外摆线Equation：方程式Evenfunction：偶函数ExpectedValued：期望值ExponentialFunction：指数函数Exponents,lawsof：指数率Extremevalue：极值ExtremeValueTheorem：极值定理Factorial：阶乘FirstDerivativeTest：一阶导数试验法Firstoctant：第一卦限Focus：焦点Fractions：分式Function：函数FundamentalTheoremofCalculus：微积分基本定理Geometricseries：几何级数Gradient：梯度Graph：图形GreenFormula：格林公式Half-angleformulas：半角公式Harmonicseries：调和级数Helix：螺旋线HigherDerivative：高阶导数Horizontalasymptote：水平渐近线Horizontalline：水平线Hyperbola：双曲线Hyperboloid：双曲面D:Decreasingfunction：递减函数Decreasingsequence：递减数列Definiteintegral：定积分Degreeofapolynomial：多项式之次数Density：密度Derivative：导数ofapositefunction：复合函数之导数ofaconstantfunction：常数函数之导数directional：方向导数domainof：导数之定义域ofexponentialfunction：指数函数之导数higher：高阶导数partial：偏导数ofapowerfunction：幂函数之导数ofapowerseries：羃级数之导数ofaproduct：积之导数ofaquotient：商之导数asarateofchange：导数当作变率right-hand：右导数second：二阶导数astheslopeofatangent：导数看成切线之斜率Determinant：行列式Differentiablefunction：可导函数Differential：微分Differentialequation：微分方程partial：偏微分方程Differentiation：求导法implicit：隐求导法partial：偏微分法termbyterm：逐项求导法Directionalderivatives：方向导数Discontinuity：不连续性Diskmethod：圆盘法Distance：距离Divergence：发散Domain：定义域Dotproduct：点积Doubleintegral：二重积分changeofvariablein：二重积分之变数变换inpolarcoordinates：极坐标二重积分C:Calculus：微积分differential：微分学integral：积分学Cartesiancoordinates：笛卡儿坐标，一般指直角坐标Cartesiancoordinatessystem：笛卡儿坐标系Cauch’sMeanValueTheorem：柯西均值定理ChainRule：连锁律Changeofvariables：变数变换Circle：圆Circularcylinder：圆柱Closedinterval：封闭区间Coefficient：系数positionoffunction：函数之合成poundinterest：复利Concavity：凹性Conchoid：蚌线Cone：圆锥Constantfunction：常数函数Constantofintegration：积分常数Continuity：连续性atapoint：在一点处之连续性ofafunction：函数之连续性onaninterval：在区间之连续性fromtheleft：左连续fromtheright：右连续Continuousfunction：连续函数Convergence：收敛intervalof：收敛区间radiusof：收敛半径Convergentsequence：收敛数列series：收敛级数Coordinate：s：坐标Cartesian：笛卡儿坐标cylindrical：柱面坐标polar：极坐标rectangular：直角坐标spherical：球面坐标Coordinateaxes：坐标轴Coordinateplanes：坐标平面Cosinefunction：余弦函数Criticalpoint：临界点Cubicfunction：三次函数Curve：曲线Cylinder：圆柱CylindricalCoordinates：圆柱坐标A、B:Absoluteconvergence：绝对收敛Absoluteextremevalues：绝对极值Absolutemaximumandminimum：绝对极大与极小Absolutevalue：绝对值Absolutevaluefunction：绝对值函数Aeleration：加速度Antiderivative：反导数Approximateintegration：近似积分Approximation：逼近法bydifferentials：用微分逼近linear：线性逼近法bySimpson’sRule：Simpson法则逼近法bytheTrapezoidalRule：梯形法则逼近法Arbitraryconstant：任意常数Arclength：弧长Area：面积underacurve：曲线下方之面积betweencurves：曲线间之面积inpolarcoordinates：极坐标表示之面积ofasectorofacircle：扇形之面积ofasurfaceofarevolution：旋转曲面之面积Asymptote：渐近线horizontal：水平渐近线slant：斜渐近线vertical：垂直渐近线Averagespeed：平均速率Averagevelocity：平均速度Axes,coordinate：坐标轴Axesofellipse：椭圆之轴Binomialseries：二项级

　　⑿求两个matlab的程序，分别利用复化梯形公式和辛普森公式求解误差函数erf(x)

　　⒀g=(t)exp(-t.^);

　　⒁x=linspace(,,);

　　⒂y=zeros(,);

　　⒃y=zeros(,);

　　⒄y(i)=/sqrt(pi)*Simpson(g,,x(i),);?%幸普森公式

　　⒅y(i)=/sqrt(pi)*trapezoidal(g,,x(i),);%复合梯形公式

　　⒆plot(x,y,’r-’,x,y,’b.’);

　　⒇legend(’辛普森公式’,’复合梯形公式’);

　　⒈functiony=Simpson(f,a,b,M)

　　⒉%f被积函数；a积分下限；b积分上限；M子区间个数（将x分为多少个区间

　　⒊h=(b-a)/(*M);

　　⒋x=a+(*i-)*h;

　　⒌forj=:(M-)

　　⒍y=h/*(f(a)+*s+*s+f(b));

　　⒎trapezoidal.m

　　⒏functiony=trapezoidal(f,a,b,n)

　　⒐h=(b-a)/n;

　　⒑x=zeros(,n+);

　　⒒F=zeros(,n+);

　　⒓x(k+)=a+k*h;

　　⒔x(k+)=^(-);

　　⒕T_=h/*(f(x())+f(x(n+)));

　　⒖F(i)=h*f(x(i));

　　⒗T_=sum(F);