1、高等数学名词（中英文）第一章函数与极限Chapter1FunctionandLimit集合set元素element子集subset空集emptyset并集union交集intersection差集differenceofset基本集basicset补集complementset直积directproduct笛卡儿积Cartesianproduct开区间openinterval闭区间closedinterval半开区间halfopeninterval有限区间finiteinterval区间的长度lengthofaninterval无限区间infiniteinterval领域neighborhoo
2、d领域的中心centreofaneighborhood领域的半径radiusofaneighborhood左领域leftneighborhood右领域rightneighborhood映射mappingX至iY的映射mappingofXontoY满射surjection单射injection一一映射one-to-onemapping双射bijection算子operator变化transformation函数function逆映射inversemapping复合映射compositemapping自变量independentvariable因变量dependentvariable定义域doma
3、in函数值valueoffunction函数关系functionrelation值域range自然定义域naturaldomain单值函数singlevaluedfunction多值函数multiplevaluedfunction单值分支one-valuedbranch函数图形graphofafunction绝对值函数absolutevalue符号函数sighfunction整数部分integralpart阶梯曲线stepcurve当且仅当ifandonlyif(iff)分段函数piecewisefunction上界upperbound下界lowerbound有界boundedness无界un
4、bounded函数的单调性monotonicityofafunction单调增加的increasing单调减少的decreasing单调函数monotonefunction函数的奇偶性parity(odevity)ofafunction对称symmetry偶函数evenfunction奇函数oddfunction函数的周期性periodicityofafunction周期period反函数inversefunction直接函数directfunction复合函数compositefunction中间变量intermediatevariable函数的运算operationoffunction基本
5、初等函数basicelementaryfunction初等函数elementaryfunction幂函数powerfunction指数函数exponentialfunction对数函数logarithmicfunction三角函数trigonometricfunction反三角函数inversetrigonometricfunction常数函数constantfunction双曲函数hyperbolicfunction双曲正弦hyperbolicsine双曲余弦hyperboliccosine双曲正切hyperbolictangent反双曲正弦inversehyperbolicsine反双曲余
6、弦inversehyperboliccosine反双曲正切inversehyperbolictangent极限limit数列sequenceofnumber收敛convergence收敛于aconvergetoa发散divergent极限的唯一性uniquenessoflimits收敛数列的有界性boundednessofaconvergentsequence子列subsequence函数的极限limitsoffunctions函数当x趋于x0时的极限limitoffunctionsasxapproachesx0左极限leftlimit右极限rightlimit单侧极限one-sidedlim
7、its水平渐近线horizontalasymptote无穷小infinitesimal无穷大infinity铅直渐近线verticalasymptote夹逼准则squeezerule单调数列monotonicsequence高阶无穷小infinitesimalofhigherorder低阶无穷小infinitesimaloflowerorder同阶无穷小infinitesimalofthesameorder等阶无穷小equivalentinfinitesimal函数的连续性continuityofafunction增量increment函数在x0连续thefunctioniscontinuou
8、satx0左连续leftcontinuous右连续rightcontinuous区间上的连续函数continuousfunction函数在该区间上连续functioniscontinuousonaninterval不连续点discontinuitypoint第一类间断点discontinuitypointofthefirstkind第二类间断点discontinuitypointofthesecondkind初等函数的连续性continuityoftheelementaryfunctions定义区间definedinterval最大值globalmaximumvalue(absolutemax
9、imum)最小值globalminimumvalue(absoluteminimum)零点定理thezeropointtheorem介值定理intermediatevaluetheorem第二章导数与微分Chapter2DerivativeandDifferential速度velocity匀速运动uniformmotion平均速度averagevelocity瞬时速度instantaneousvelocity圆的切线tangentlineofacircle切线tangentline切线的斜率slopeofthetangentline位置函数positionfunction导数derivativ
10、e可导derivable函数的变化率问题problemofthechangerateofafunction导函数derivedfunction左导数left-handderivative右导数right-handderivative单侧导数one-sidedderivatives在闭区间a,b上可导isderivableontheclosedintervala,b切线方程tangentequation角速度angularvelocity成本函数costfunction边际成本marginalcost链式法则chainrule隐函数implicitfunction显函数explicitfunct
12、bsoluteerror相对误差relativeerror第三章微分中值定理与导数的应用Chapter3MeanValueTheoremofDifferentialsandtheApplicationofDerivatives罗马定理Rollestheorem费马引理Fermatslemma拉格朗日中值定理Lagrangesmeanvaluetheorem驻点stationarypoint稳定点stablepoint临界点criticalpoint辅助函数auxiliaryfunction拉格朗日中值公式Lagrangesmeanvalueformula柯西中值定理Cauchysmeanval
13、uetheorem洛必达法则LHospitalsRule0/0型不定式indeterminateformoftype0/0不定式indeterminateform泰勒中值定理Taylorsmeanvaluetheorem泰勒公式Taylorformula余项remainderterm拉格朗日余项Lagrangeremainderterm麦克劳林公式Maclaurinsformula佩亚诺公式Peanoremainderterm凹凸性concavity凹向上的concaveupward,cancaveup凹向下的，向上凸的concavedownwardconcavedown拐点inflectio
14、npoint函数的极值extremumoffunction极大值local(relative)maximum最大值global(absolute)mximum极小值local(relative)minimum最小值global(absolute)minimum目标函数objectivefunction曲率curvature弧微分arcdifferential平均曲率averagecurvature曲率园circleofcurvature曲率中心centerofcurvature曲率半径radiusofcurvature渐屈线evolute渐伸线involute根的隔离isolationofro
15、ot隔离区间isolationinterval切线法tangentlinemethod第四章不定积分Chapter4IndefiniteIntegrals原函数primitivefunction(anti-derivative)积分号signofintegration被积函数integrand积分变量integralvariable积分曲线integralcurve积分表tableofintegrals换元积分法integrationbysubstitution分部积分法integrationbyparts分部积分公式formulaofintegrationbyparts有理函数rationa
16、lfunction真分式properfraction假分式improperfraction第五章定积分Chapter5DefiniteIntegrals曲边梯形trapezoidwith曲边curveedge窄矩形narrowrectangle曲边梯形的面积areaoftrapezoidwithcurvededge积分下限lowerlimitofintegral积分上限upperlimitofintegral积分区间integralinterval分割partition积分和integralsum可积integrable矩形法rectanglemethod积分中值定理meanvaluetheo
17、remofintegrals函数在区间上的平均值averagevalueofafunctiononanintegvals牛顿莱布尼茨公式Newton-Leibnizformula微积分基本公式fundamentalformulaofcalculus换元公式formulaforintegrationbysubstitution递推公式recurrenceformula反常积分improperintegral反常积分发散divergent反常积分收敛convergent无穷限的反常积分infiniteinterval无界函数的反常积分unboundedfunctions绝对收敛theimprope
18、rintegralistheimproperintegralisimproperintegralonanimproperintegralofabsolutelyconvergent第六章定积分的应用Chapter6ApplicationsoftheDefiniteIntegrals元素法theelementmethod面积元素elementofarea平面图形的面积areaofaluanefigure直角坐标又称“笛卡儿坐标(Cartesiancoordinates)”极坐标polarcoordinates抛物线parabola椭圆ellipse旋转体的面积volumeofasolidofro
19、tation旋转椭球体ellipsoidofrevolution,ellipsoidofrotation曲线的弧长arclengthofacurve可求长的rectifiable光滑smooth功work水压力waterpressure引力gravitation变力variableforce第七章空间解析几何与向量代数Chapter7SpaceAnalyticGeometryandVectorAlgebra向量vector自由向量freevector单位向量unitvector零向量zerovector相等equal平行parallel向量的线性运算linearpoerationofvecto
20、r三角法则trianglerule平行四边形法则parallelogramrule交换律commutativelaw结合律associativelaw负向量negativevector差difference分配律distributivelaw空间直角坐标系spacerectangularcoordinates坐标面coordinateplane卦限octant向量的模modulusofvector向量a与b的夹角anglebetweenvectoraandb方向余弦directioncosine方向角directionangle向量在轴上的投影projectionofavectorontoan
21、axis数量积，外积，叉积scalarproduct,dotproduct,innerproduct曲面方程equationforasurface球面sphere旋转曲面surfaceofrevolution母线generatingline轴axis圆锥面cone顶点vertex旋转单叶双曲面revolutionhyperboloidsofonesheet旋转双叶双曲面revolutionhyperboloidsoftwosheets柱面cylindricalsurface,cylinder圆柱面cylindricalsurface准线directrix抛物柱面paraboliccylinde
22、r二次曲面quadricsurface椭圆锥面dllipticcone椭球面ellipsoid单叶双曲面hyperboloidofonesheet双叶双曲面hyperboloidoftwosheets旋转椭球面ellipsoidofrevolution椭圆抛物面ellipticparaboloid旋转抛物面paraboloidofrevolution双曲抛物面hyperbolicparaboloid马鞍面saddlesurface椭圆柱面ellipticcylinder双曲柱面hyperboliccylinder抛物柱面paraboliccylinder空间曲线spacecurve空间曲线的一
23、般方程generalformequationsofaspacecurve空间曲线的参数方程parametricequationsofaspacecurve螺转线spiral螺矩pitch投影柱面projectingcylinder投影projection平面的点法式方程pointnormformeqyationofaplane法向量normalvector平面的一般方程generalformequationofaplane两平面的夹角anglebetweentwoplanes点到平面的距离distancefromapointtoaplane空间直线的一般方程generalequationofa
24、lineinspace方向向量directionvector直线的点向式方程pointdirectionformequationsofaline方向数directionnumber直线的参数方程parametricequationsofaline两直线的夹角anglebetweentwolines垂直perpendicular直线与平面的夹角anglebetweenalineandaplanes平面束pencilofplanes平面束的方程equationofapencilofplanes行列式determinant系数行列式coefficientdeterminant第八章多元函数微分法及其
25、应用Chapter8DifferentiationofFunctionsofSeveralVariablesandItsApplication一元函数functionofonevariable多元函数functionofseveralvariables内点interiorpoint外点exteriorpoint边界点frontierpoint,boundarypoint聚点pointofaccumulation开集openset闭集closedset连通集connectedset开区域openregion闭区域closedregion有界集boundedset无界集unboundedsetn维
26、空间n-dimentionalspace二重极限doublelimit多元函数的连续性continuityoffunctionofseveal连续函数continuousfunction不连续点discontinuitypoint一致连续uniformlycontinuous偏导数partialderivative对自变量x的偏导数partialderivativewithrespecttoindependentvariablex高阶偏导数partialderivativeofhigherorder二阶偏导数secondorderpartialderivative混合偏导数hybridpart
27、ialderivative全微分totaldifferential偏增量oartialincrement偏微分partialdifferential全增量totalincrement可微分differentiable必要条件necessarycondition充分条件sufficientcondition叠加原理superpostitionprinciple全导数totalderivative中间变量intermediatevariable隐函数存在定理theoremoftheexistenceofimplicitfunction曲线的切向量tangentvectorofacurve法平面no
28、rmalplane向量方程vectorequation向量值函数vector-valuedfunction切平面tangentplane法线normalline方向导数directionalderivative梯度gradient数量场scalarfield梯度场gradientfield向量场vectorfield势场potentialfield引力场gravitationalfield引力势gravitationalpotential曲面在一点的切平面tangentplanetoasurfaceatapoint曲线在一点的法线normallinetoasurfaceatapoint无条件极
29、值unconditionalextremevalues条件极值conditionalextremevalues拉格朗日乘数法Lagrangemultipliermethod拉格朗日乘子Lagrangemultiplier经验公式empiricalformula最小二乘法methodofleastsquares均方误差meansquareerror第九章重积分Chapter9MultipleIntegrals二重积分doubleintegral可加性additivity累次积分iteratedintegral体积元素volumeelement三重积分tripleintegral直角坐标系中的体积
30、元素volumeelementinrectangularcoordinatesystem柱面坐标cylindricalcoordinates柱面坐标系中的体积元素volumeelementincylindricalcoordinatesystem球面坐标sphericalcoordinates球面坐标系中的体积元素volumeelementinsphericalcoordinatesystem反常二重积分improperdoubleintegral曲面的面积areaofasurface质心centreofmass静矩staticmoment密度density形心centroid转动惯量mome
31、ntofinertia参变量parametricvariable第十章曲线积分与曲面积分Chapter10Line(Curve)IntegralsandSurfaceIntegrals对弧长的曲线积分lineintegralswithrespecttoarchength第一类曲线积分lineintegralsofthefirsttype对坐标的曲线积分lineintegralswithrespecttox,y,andz第二类曲线积分lineintegralsofthesecondtype有向曲线弧directedarc单连通区域simpleconnectedregion复连通区域complex
32、connectedregion格林公式Greenformula第一类曲面积分surfaceintegralsofthefirsttype对面的曲面积分surfaceintegralswithrespecttoarea有向曲面directedsurface对坐标的曲面积分surfaceintegralswithrespecttocoordinateelements第二类曲面积分surfaceintegralsofthesecondtype有向曲面元elementofdirectedsurface高斯公式gaussformula拉普拉斯算子Laplaceoperator格林第一公式Greensfi
33、rstformula通量flux散度divergence斯托克斯公式Stokesformula环流量circulation旋度rotation,curl第十一章无穷级数Chapter11InfiniteSeries一般项generalterm部分和partialsum余项remainderterm等比级数geometricseries几何级数geometricseries公比commonratio调和级数harmonicseries柯西收敛准则Cauchyconvergencecriteria,Cauchycriteriaforconvergence正项级数seriesofpositivete
34、rms达朗贝尔判别法DAlemberttest柯西判别法Cauchytest交错级数alternatingseries绝对收敛absolutelyconvergent条件收敛conditionallyconvergent柯西乘积Cauchyproduct函数项级数seriesoffunctions发散点pointofdivergence收敛点pointofconvergence收敛域convergencedomain和函数sumfunction幂级数powerseries幂级数的系数coeffcientsofpowerseries阿贝尔定理AbelTheorem收敛半径radiusofconv
35、ergence收敛区间intervalofconvergence泰勒级数Taylorseries麦克劳林级数Maclaurinseries二项展开式binomialexpansion近似计算approximatecalculation舍入误差round-offerror,roundingerror欧拉公式Eulersformula魏尔斯特拉丝判别法Weierstrasstest三角级数trigonometricseries振幅amplitude角频率angularfrequency初相initialphase矩形波squarewave谐波分析harmonicanalysis直流分量direct
36、component基波fundamentalwave二次谐波secondharmonic三角函数系trigonometricfunctionsystem傅立叶系数Fouriercoefficient傅立叶级数Forrierseries周期延拓periodicprolongation正弦级数sineseries余弦级数cosineseries奇延拓oddprolongation偶延拓evenprolongation傅立叶级数的复数形式complexformofFourierseries第十二章微分方程Chapter12DifferentialEquation解微分方程solveadifferen
37、tialequation常微分方程ordinarydifferentialequation偏微分方程partialdifferentialequation,PDE微分方程的阶orderofadifferentialequation微分方程的解solutionofadifferentialequation微分方程的通解generalsolutionofadifferentialequation初始条件initialcondition微分方程的特解particularsolutionofadifferentialequation初值问题initialvalueproblem微分方程的积分曲线int
38、egralcurveofadifferentialequation可分离变量的微分方程variableseparabledifferentialequation隐式解implicitsolution隐式通解inplicitgeneralsolution衰变系数decaycoefficient衰变decay齐次方程homogeneousequation一阶线性方程lineardifferentialequationoffirstorder非齐次non-homogeneous齐次线性方程homogeneouslinearequation非齐次线性方程non-homogeneouslinearequ
39、ation常数变易法methodofvariationofconstant暂态电流transientstatecurrent稳态电流steadystatecurrent伯努利方程Bernoulliequation全微分方程totaldifferentialequation积分因子integratingfactor高阶微分方程differentialequationofhigherorder悬链线catenary高阶线性微分方程lineardifferentialequationofhigherorderfreevibration强迫振动的微分方程differentialequationof自由
41、neardifferentialequationwithvariablecoefficient特征方程characteristicequation无阻尼自由振动的微分方程differentialequationoffreevibrationwithzerodamping固有频率naturalfrequency简谐振动simpleharmonicoscillation,simpleharmonicvibration微分算子differentialoperator待定系数法methodofundeterminedcoefficient共振现象resonancephenomenon欧拉方程Euler
42、equation幂级数解法powerseriessolution数值解法numerialsolution勒让德方程Legendreequation微分方程组systemofdifferentialequations常系数线性微分方程组systemoflineardifferentialequationswithconstantcoefficientV、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：
43、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Sec
44、ondDerivativeTest：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Squee
45、zeTheorem：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Rectang
46、ularcoordinates：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：拋物线Paraboliccylinder：抛物柱面Paraboloid：抛物面Paralle
47、lepiped：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Polareq
48、uation：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Nat
49、uralnumber：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-handlim
50、it：左极限Lemniscate：双钮线Length：长度Levelcurve：等高线LHospitalsrule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Lo
51、garithmicfunction：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Inst
52、antaneousvelocity：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Equatio
53、n：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
54、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ofacompositefunction：复合函数之导数ofaconstantf
55、unction：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Differentia
56、l：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differ
57、ential：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CauchsMeanValueTheorem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Compositionoffunction：函数之合成Compoundinterest：复利Concavity：凹性Conchoid：蚌线Cone：圆锥Constantfuncti
58、on：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
59、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Acceleration：加
60、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bySimpsonsRule：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ofasurfaceofarevol