81. Calculus Integral calculus of functions of several variables multiple Vector integral calculus vector fields; line integrals in the plane;...... http://www.westerncalendar.uwo.ca/western/web/2005(new)/Courses_UWO_CALCULUS.htm

@import "style_css2.css"; Registrar's Office UWO Home Table of Contents Academic Calendar 2005 (new) ... AFFILIATED COLLEGES Calculus Calculus Courses 050a/b 051a/b 081a/b 091a/b ... 281a/b Calculus 050a/b, 051a/b, and 081a/b, 250a/b, 251a/b, 280a/b, and 281a/b are offered jointly by the Departments of Applied Mathematics and Mathematics. Calculus 091a/b is offered by the Department of Applied Mathematics. For course descriptions of other mathematics courses at the Year 1 and senior levels, please refer to the course listing in APPLIED MATHEMATICS (S) DIFFERENTIAL EQUATIONS (S) LINEAR ALGEBRA (S) and MATHEMATICS (S) Calculus 050a/b, Calculus I Description: Review of limits and derivatives of exponential, logarithmic and rational functions. Trigonometric functions and their inverses. The derivatives of the trig functions and their inverses. L'Hospital's rules. The definite integral. Fundamental theorem of Calculus. Simple substitution. Applications including areas of regions and volumes of solids of revolution. Antirequisite(s): Mathematics 030 Applied Mathematics 026 Prerequisite(s): Grade 12U Advanced Functions and Introductory Calculus (MCB4U) or OAC Calculus or Mathematics 012a/b 4 lecture hours, 0.5 course.

82. Primus: Problems, Resources, And Issues In Mathematics Undergraduate Studies: Cl Full text of the article, Classroom integral calculus Some usefule digressions when teaching integral calculus from Primus Problems, Resources, http://www.findarticles.com/p/articles/mi_qa3997/is_200203/ai_n9076419

@import url(/css/us/style1.css); @import url(/css/us/searchResult1.css); @import url(/css/us/articles.css); @import url(/css/us/artHome1.css); Advanced Search Home Help IN free articles only all articles this publication Automotive Sports 10,000,000 articles - not found on any other search engine. FindArticles Primus: Problems, Resources, and Issues in Mathematics Undergraduate Studies Mar 2002 Content provided in partnership with 10,000,000 articles Not found on any other search engine. Featured Titles for ASA News ASEE Prism Academe African American Review ... View all titles in this topic Hot New Articles by Topic Automotive Sports Top Articles Ever by Topic Automotive Sports Classroom integral calculus: Some usefule digressions when teaching integral calculus Primus: Problems, Resources, and Issues in Mathematics Undergraduate Studies Mar 2002 by Acosta, Daniel J Wills, Randall Save a personal copy of this article and quickly find it again with Furl.net. It's free! Save it. CLASSROOM INTEGRAL CALCULUS: SOME USEFUL DIGRESSIONS WHEN TEACHING INTEGRAL CALCULUS* ABSTRACT: In this article we outline ideas and exercises for two topics that accompany the standard treatment of integral calculus. These concepts emphasize intuition to help facilitate student comprehension of the definite integral as a limit of Riemann sums.

83. Integral Calculus - Columbia Encyclopedia® Article About Integral Calculus Columbia Encyclopedia® article about integral calculus. integral calculus. Information about integral calculus in the Columbia Encyclopedia®. http://columbia.thefreedictionary.com/integral calculus

Domain='thefreedictionary.com' word='integral calculus' Your help is needed: American Red Cross The Salvation Army join mailing list webmaster tools Word (phrase): Word Starts with Ends with Definition subscription: Dictionary/ thesaurus Computing dictionary Medical dictionary Legal dictionary Financial dictionary Acronyms Columbia encyclopedia Wikipedia encyclopedia Hutchinson encyclopedia integral calculus Also found in: Dictionary/thesaurus Medical Wikipedia Hutchinson 0.03 sec. Page tools Printer friendly Cite / link Email Feedback integral calculus: see calculus calculus, Click the link for more information. Mentioned in References in classic literature Belidor, Bernard Forest de calculus Cavalieri, Francesco Bonaventura mathematics Because it will be trying to solve the problem called `the problem of the three bodies,' for which the integral calculus is not yet far enough advanced. Round The Moon by Verne, Jules View in context More results Columbia browser Full browser insulin shock Insull, Samuel insurance Insurgents ... integer integral calculus integrated circuit Integrated Pest Management integration integumentary system ... Integral 3 (Tenovis) integral calculus Integral closure Integral Coach Factory (India) Integral Components Of End Items Integral curve ... Integral Gateway Word (phrase): Word Starts with Ends with Definition Free Tools: For surfers: Browser extension Word of the Day NEW!

84. Math 52 - Integral Calculus Of Several Variables - Fall 2004 Math 52 Integral calculus of Several Variables - Fall 04. General Info Syllabus Homework Announcements Dates Additional Help Solutions http://math.stanford.edu/~brubaker/math52.html

Math 52 - Integral Calculus of Several Variables - Fall '04 General Info Additional Help General Information Meeting Time Mon., Tue., Wed., Thu., Fri., 2:15 - 3:05 Location Building 380 (Math), room 380-X Professor Ben Brubaker ( brubaker@math.stanford.edu Office: 382-F (2nd floor, Math building 380) Office Phone: 3-4507 Office Hours: We'll discuss best times in class Course Assistants Robin Oliver-Jones - Room 380-H Office Hours: Mon. 9-11 a.m., Tue., Thu. 3:05-5 p.m. Yu-jong Tzeng - Room 380-L Office Hours: Mon. 3:30-5 p.m., Tue. 9-10:30 a.m. Textbook Multivariable Calculus (With Matrices) , by Edwards and Penney, 6th edition. Required and available at the bookstore. Grade Breakdown Homework: 1/8 Midterm I: 3/16 Integration Quiz: 1/16 Midterm II: 1/4 Final Exam: 3/8 Course Content We will investigate several generalizations of the one-variable integration taught in first calculus courses. These include iterated integrals, line and surface integrals, and vector analysis. The goal will be a unified picture of integration theory as expressed in the theorems of Green, Gauss, and ultimately Stokes. Prerequisites Math 51 or its equivalent A brief list of topics you should be comfortable with (but will be briefly reviewed throughout the course as necessary): (partial) derivatives, single variable integration techniques, vector operations, matrices and basic linear algebra.

85. MATH 214-2 - INTEGRAL CALCULUS INTEGRAL calculus. Miguel A. Lerma Fall 2004. Section 61 Definite integrals and areas, the Fundamental Theorems of calculus, substitution, http://www.math.northwestern.edu/~mlerma/courses/math214-2-04f/

MATH 214-2 INTEGRAL CALCULUS Miguel A. Lerma - Fall 2004 Section 61 MWF 12:00 noon - ANNEN G15 TH 12:00 noon - LUNT 104/107 http://www.math.northwestern.edu/~mlerma/courses/math214-2-04f/ This is the web page for MATH 214-2, section 61, Fall 2004 Consult it often for announcements, homework assignments and possible changes to the syllabus. Index Announcements Course description Teachers Instructor ... List of Grades Announcements Final Exam: Thursday, December 9th, 2004, 12:00 noon - 2:00 pm, Coon Forum. Course Description Math 214-2 Calculus II Definite integrals and areas, the Fundamental Theorems of Calculus, substitution, integration by parts, other methods of integration, numerical techniques, computation of volumes, arc length, average of a function, applications (to physics, engineering, and probability), separable differential equations, exponential growth, infinite series, and Taylor series. Teachers Instructor Teaching Assistants Name Miguel A. Lerma Mike Greene Fang Wang Office Lunt 203 Phone E-mail mlerma@math.northwestern.edu

86. MATH 214-2 - INTEGRAL CALCULUS INTEGRAL calculus. Miguel A. Lerma Fall 2003. Section 31 Definite integrals and areas, the Fundamental Theorems of calculus, substitution, http://www.math.northwestern.edu/~mlerma/courses/math214-2-03f/

MATH 214-2 INTEGRAL CALCULUS Miguel A. Lerma - Fall 2003 Section 31 MWF 9:00 am - Lunt 105 TH 9:00 am - LUNT 105/107 http://www.math.northwestern.edu/~mlerma/courses/math214-2-03f/ This is the web page for MATH 214-2, section 31, Fall 2003 Consult it often for announcements, homework assignments and possible changes to the syllabus. Index Announcements Course description Teachers Instructor ... List of Grades Announcements Final Exam : Thursday, December 11, 2003, 3:00-5:00pm, Tech M345. Course Description Math 214-2 Calculus II Definite integrals and areas, the Fundamental Theorems of Calculus, substitution, integration by parts, other methods of integration, numerical techniques, computation of volumes, arc length, average of a function, applications (to physics, engineering, and probability), separable differential equations, exponential growth, infinite series, and Taylor series. Teachers Instructor Teaching Assistants Name Miguel A. Lerma Valentina Joukhovitski Radu V. Saghin Office Lunt 203 Lunt B20 Lunt B13 Phone E-mail mlerma@math.northwestern.edu

87. Calculus -- Facts, Info, And Encyclopedia Article Integral calculus is the mirror image of differential calculus. Examples of integral calculus problems include finding the following quantities http://www.absoluteastronomy.com/encyclopedia/c/ca/calculus.htm

Calculus [Categories: Academic disciplines, Calculus] For other uses of the term calculus see (Click link for more info and facts about calculus (disambiguation)) calculus (disambiguation) Calculus is a central branch of (A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement) mathematics , developed from (The mathematics of generalized arithmetical operations) algebra and (The pure mathematics of points and lines and curves and surfaces) geometry , and built on two major complementary ideas. One concept is called differential calculus . It studies rates of change, which are usually illustrated by the (An elevated geological formation) slope of a line. Differential calculus is based on the problem of finding the instantaneous rate of change of one quantity relative to another. Examples of typical differential calculus problems are finding the following quantities: The acceleration and speed of a free-falling body at a particular moment. The loss in speed and trajectory of a fired projectile, such as an artillery shell or bullet. Change in profitability over time of a growing business at a particular point.

88. Math 252 -- Integral Calculus -- OSU Extended Campus -- Oregon State University OSU Extended Campus Oregon State University. MTH 252 Integral calculus. Go to Lesson. A main concept of Integral calculus. Go to Lesson. http://oregonstate.edu/instruct/mth252/Jwlee/252_400_VPR/cq2/

Go to Lesson. . . 1 Antidifferentiation and Indefinite Integals 2 Introduction To Differential Equations 3 Sums, Area and Distance 4 Riemann Sums and the Definite Integral 5 The First Fundamental Theorem of Calculus 6 The second Fundamental Theorem of Calculus 7 Evaluating Definite Integrals 8 The Area of a Plane Region 9 Volumes of Solids (Slabs, Disks, Washers) 10 Volumes of Solids of Revolution (Shells) 11 Length of a Plane Curve 12 Work 13 Moments, Center of Mass 14 Exponential and Logarithmic Functions 15 Exponential Growth and Decay 16 Inverse Trigonometric Functions 17 Integration by Substitution 18 Some Trigonometric Integrals 19 Rationalizing Substitutions 20 Integration by Parts 21 Integration of Rational Functions 22 Numerical Integration Home page Resources Communications Calendar Welcome! Instructor: John W. Lee Course Information Lesson Plan Getting Started ... Blackboard A main concept of Integral Calculus Go to Lesson. . . 1 Antidifferentiation and Indefinite Integals 2 Introduction To Differential Equations 3 Sums, Area and Distance

89. Calculus The integral calculus makes great use of the Fundamental Theorem, These topics in differential and integral calculus may form a course in Advanced http://www.du.edu/~jcalvert/math/calculus.htm

The Elements of Calculus Calculus is the foundation of the modern mathematics of physics and engineering Calculus was invented by Newton and Leibnitz at the end of the 17th century. While algebra had been an important addition to mathematics in the immediately preceding centuries, it provided mainly a notational convenience. A very significant convenience, to be sure, but it did not provide much additional power to mathematical investigations. Calculus, however, changed mathematics radically, and possessed great power and range, in practical matters as well as theoretical. Calculus involves a convenient representation of certain limiting processes, which were hinted at in earlier mathematics, but were very difficult to use, and then only in particular problems. In the educational curriculum for science and engineering, calculus forms a bridge between elementary mathematics, such as geometry, algebra and trigonometry, and advanced mathematics, such as differential equations, vector analysis and complex variables. In this position, it has other duties to perform other than simply introducing its elements. To begin the study of calculus, concepts of function, continuous function and limits are necessary, as well as some idea of the nature of mathematical proof. During the course, the student also should be introduced to the theory of curves, infinite series, power series, elementary functions, convergence, Fourier series, and other topics, as examples to which calculus can be applied. Finally, the course should foster manipulative skills, and even introduce numerical methods, such as differencing and quadrature. In all this, the central idea of calculus tends to be obscured.

90. 2004/05 Calendar, Course Descriptions-Mathematics & Computer Science, Division O MAE208. Elements of Integral calculus (and Linear Algebra). This course will cover the rules of integral calculus, including lessons on antiderivatives and http://www.rmc.ca/academic/continuing/calendar/courses/mae208_e.htm

dqmcodebase = "/academic/continuing/script/" DCS Home Table of Contents General Information on Continuing Studies Academic Programmes ... DCS Forms DCS Calendar 2005 - 2006 PDF Elements of Integral Calculus (and Linear Algebra) This course will cover the rules of integral calculus, including lessons on antiderivatives and indefinite integration, rules of integration (substitution and integration by parts), Riemann sums, definite integrals and the Fundamental Theorem of Calculus, numerical techniques for approximating definite integrals, applications of definite integrals to problems in business and economics, and to the evaluation of probabilities and expected values, improper integrals and their evaluation, linear systems of equations and their solutions, matrices and matrix operations, matrix representation of linear systems, and Gaussian elimination. Programme: For Second Year students taking Arts. This course cannot be used for credit in support of a degree in Science or Engineering. in development 1 credit To order textbooks Campus Bookstore Site Map Date Modified: 2005/04/04 Important Notices

91. Hobe Sound Bible College - Syllabus - Integral Calculus integral calculus. F. can define, in his own words, specified key concepts G. can label statements about integral calculus as being either true or http://www.hsbc.edu/syllabi/MA2140.htm

HOBE SOUND BIBLE COLLEGE Integral Calculus H.E. Hannold sem hrs) Sem II (2004-2005) Class Time: 10:00 - 10:55 AM ( T ,Th hehannold@hsbc.edu Room 104 Office Hours: 7:00 - 8:20 AM ( T ,Th I. Mission Statement The mission of Hobe Sound Bible College is to provide a Christ-centered, Bible- based education in the Wesleyan tradition which prepares servant-leaders who think Biblically, live spirit-filled lives, fulfill the Great Commission, and glorify God in all they do. II. Course Description This course is part of the mathematics major core. God's order is shown through the definite integral, the fundamental theorem of calculus, natural logarithm, area, arc length, convergent tests, power series and differential equations. III. Objectives The student: A. can testify to a personal relationship with our ever changing, changeless Lord. B. will rate himself as having a positive attitude toward calculus. C. will evaluate himself as positively seeing how all mathematical truth points to the unity which is centered in God. D. will evaluate himself as being thankful for the variety of ways to obey Biblical principles and mathematical principles.

92. Comprehensive Ratings And Review Of Calculus Web Sites All of Differential and Integral calculus, including other maths topics Precalculus, Differential and Integral calculus and also Linear Algebra http://www.csam.montclair.edu/mathsci/classroom/math_project_desc.htm

No. Title Type Authors/Producers Topics Calculus @ internet Comprehensive Link List Categorized Links Searchable Links WebPrimitives, Cambridge, MA, www.webprimitives.com All of Differential and Integral Calculus, including other maths topics Link : www.calculus.net Comments: Excellent Site. Links are categorized according to calculus topics and are also searchable. Links include courses from Algebra to graduate school, and also teacher resources such as technology, pedagogy, and reference materials. A few of the pages are still under construction. The site provides a service called Mathmarks, a free login service, which keeps your personalized list of links handy so they are available from anywhere you have web access. The Calculus Page Comprehensive Link List Categorized Links Problem Sets with answers Animations (QuickTime) Study Skills Math-related Jobs UC Davis, The Morgan Foundation, and Williams College, Joel Hass Department of Mathematics University of California All of Differential Calculus, some Integral Calculus

93. Natural Logarithms Calculus That is, it is clear (and is the fundamental theorem of integral calculus) that integral calculus is that you may integrate terms of a sum independently http://www.newton.dep.anl.gov/askasci/math99/math99065.htm

Ask A Scientist Mathematics Archive Natural Logarithms Calculus Back to Mathematics Ask A Scientist Index NEWTON Homepage Ask A Question ... NEWTON is an electronic community for Science, Math, and Computer Science K-12 Educators. Argonne National Laboratory, Division of Educational Programs, Harold Myron, Ph.D., Division Director.

94. The Carnegie Pulse: Pulse Scheduler: 21-120 Differential And Integral Calculus 21120 Differential and Integral calculus calculus Early Transcendentals (with CD-ROM) Sections 1, A, B, S H, taxes**, Total http://www.tcpulse.com/psched/course/21120/

about the carnegie pulse advertise contact subscriptions ... join news opinions events classifieds course schedule home pulse scheduler departments mathematical sciences ... View times Find course by title: google_ad_client = "pub-4008485580655165"; google_alternate_ad_url = "http://tcpulse.com/ads/"; google_ad_width = 120; google_ad_height = 240; google_ad_format = "120x240_as"; google_ad_channel ="0311748454"; google_color_border = "CCCCCC"; google_color_bg = "FFFFFF"; google_color_link = "000000"; google_color_url = "666666"; google_color_text = "333333"; //> 21-120 Differential and Integral Calculus Units: Department: Mathematical Sciences Special permission: Yes Notes: -4/W/X are taught at the Qatar Campus Related URLs: http://www.math.cmu.edu Functions, limits, derivatives, logarithmic, exponential, and trigonometric functions, inverse functions; L'Hospital's Rule, curve sketching, Mean Value Theorem, related rates, linear and quadratic approximations, maximum-minimum problems, inverse functions, definite and indefinite integrals, and hyperbolic functions; applications of integration, integration by substitution and by parts. 3 hrs lec., 2 hrs. rec. Discuss this course Textbook prices Popularity index Rank for this semester: Rank in this department: Students also scheduled 76-101 Interpretation and Argument 99-101 Computing Skills Workshop 99-102 Computing Skills Workshop 09-105 Introduction to Modern Chemistry I ... 15-100 Introductory/Intermediate Programmi...

95. Integral Calculus --  Britannica Concise Encyclopedia - Your Gateway To All Br integral calculus body Branch of calculus concerned with the theory and applications of integrals. http://concise.britannica.com/ebc/article-9368035

Home Browse Store Help Search Britannica Concise Again integral calculus  Concise Encyclopedia Article Page 1 of 1 Branch of calculus concerned with the theory and applications of integral s. While differential calculus focuses on rates of change, such as slopes of tangent lines and velocities, integral calculus deals with total size or value, such as lengths, areas, and volumes. The two branches are connected by the fundamental theorem of calculus , which shows how a definite integral is calculated by using its antiderivative (a function whose rate of change, or derivative, equals the function being integrated). For example, integrating a velocity function yields a distance function, which enables the distance traveled by an object over an interval of time to be calculated. As a result, much of integral calculus deals with the derivation of formulas for finding antiderivatives. The great utility of the subject emanates from its use in solving differential equation s. var mm = [["Jan.","January"],["Feb.","February"],["Mar.","March"],["Apr.","April"],["May","May"],["June","June"],["July","July"],["Aug.","August"],["Sept.","September"],["Oct.","October"],["Nov.","November"],["Dec.","December"]]; To cite this page: MLA style: "integral calculus."

96. Distance Calculus At Suffolk University • Course Syllabi Includes topics in differential and integral calculus as a survey/introduction Topics include a continuing study of differential and integral calculus. http://www.distancecalculus.com/syllabi/

Questions? E-Mail : info@distancecalculus.com or AIM/Chat : DistanceCalculus or Call Us @ [USA] 617.497.2096 Home Main Calculus Sequence Liberal Arts Calculus Introduction to Computer Science - ... How Quickly Can I Finish The Course? Celebrating Our 8th Year of Teaching On-Line Suffolk University is a fully-accredited university -one of the "big 25" universities in Boston, Massachusetts- Internationally known for its Law and Management Schools All Distance Calculus Courses are offered through the Computer Science Department at Suffolk University. Syllabi Liberal Arts Courses Mathematics 134 - Business Calculus [3 Units] Course Description: Functions, graphs, analytic geometry of lines and circles, limits, continuity, derivatives, differential calculus of algebraic, exponential, and logarithmic functions; applications to rate problems, maxima and minima and curve sketching, area, integral as a function, accumulation, integration techniques. Prerequisites: Precalculus Mathematics. Topics in algebra. Includes topics in differential and integral calculus as a survey/introduction course to calculus for non-science, liberal arts and business-related majors.

97. Mathematics - A.P. Intro To Integral Calculus (B) Shelby County Board of Education. Shelby County Public Schools Curriculum. Mathematics AP Intro to Integral calculus (B) http://www.shelby.k12.ky.us/Curriculum/CR15494.HTM

Index Arts/Humanities Dance Drama/Theatre ... Visual Arts Mathematics Grade K Grade 1 Grade 2 Grade 3 ... A.P. Intro to Differential Calculus (A) A.P. Intro to Integral Calculus (B) Geometry Introduction Ordering Info Made with Curriculum Designer by Scantron Corporation Shelby County Board of Education Shelby County Public Schools Curriculum Mathematics - A.P. Intro to Integral Calculus (B) Printable Version Goals and Descriptions Calculus and Pre-Calculus Information Literacy Skills ... Problem Solving Calculus and Pre-Calculus Calculus and Pre-Calculus Description Apply Calculus Concepts: Sums The learner will be able to compute area values through the evaluation of sums and application of sigma notation. Integration: Define/Apply The learner will be able to make definitions of and use properties of the definite integral. Integration: Natural Log The learner will be able to interpret the natural log ( l/x ) as the area under the curve of the function f(x) = 1/x. Integration: Define/Use/Properties The learner will be able to state the definition of the antiderivative and use its properties in problems. Integration: Estimate/Areas The learner will be able to estimate areas through the application of inscribed rectangles, circumscribed rectangles, trapezoids, and other suitable techniques.

98. MAPLE PROJECTS FOR THE FIRST YEAR OF CALCULUS There after, the fundamental theorem of integral calculus provides methods for evaluating Techniques use simple differential and integral calculus. http://www.math.gatech.edu/~bourbaki/MapleProjects.html

Maple explorations for Differential Calculus The following items are a collection of mathematical explorations developed for Georgia Tech's Math 1507. They are all formatted with Maple V. Release 4. These worksheets are ready to use, without much prior knowledge of Maple. As you read through them, you simply have to press ENTER to perform the calculations, and if you don't know Maple already you will easily begin learning how it works. After reading through a given worksheet, you can generate your own models and alternative scenarios by cutting and pasting Maple code. In each worksheet a model is introduced with a description of the content and of the level of presentation. These may be down-loaded onto your computer as text files, opened with Maple, and saved as active worksheets. Alternately, you may configure your Web browser to launch Maple as you choose a file. An Introduction to Maple : A modest worksheet to get started, by showing how to define and plot functions. Drawing Graphs : One of the primary uses of the computer will be to give visualization. This worksheet gives syntax for drawing graphs. The

99. Mathematics 2: Differential And Integral Calculus -- Index Mathematics 2 Differential and Integral calculus. http://aivwww.ugent.be/Studentenadministratie/Studiegids/2005/EN/FACULTY/LA/COUR

Mathematics 2: Differential and Integral Calculus Reference Lectured in First Year Bachelor of Bioscience Engineering Theory (A) Exercises (B) Training and projects (C) Studytime (D) Studypoints (E) Level Credit Contract? Access is determined by lecturer Examination Contract? Access is determined by lecturer Language of instruction Dutch Lecturer Jean-Pierre Ottoy Department Co-lecturers Key Words Differential and integral calculus (mathematical analysis) Objectives To teach students the most essential mathematical techniques, methods and skills, starting from a clearly defined level of foreknowledge. In this way students should be able to explore problems in their study field (bio-engineer) with a certain degree of exactness and to understand, to analyse and describe the different biological systems and production processes. A solid mathematical background needed in almost all engineering disciplines is surely based on an integral and differential calculus. (see table of contents). It is important that the students learn how to reason in a critical, logical, deductive and analytical way, without losing their sense for generality and abstraction. The subject matter of this course stimulates students to synthesize, plan and to work independently, essential qualities in the context of long-life learning. Various examples and exercises illustrate the theory. The proofs are restricted to a necessary minimum. Contents 1. Series

100. Integral Calculus Integral calculus. Indefinite Integrals. Definition A function F(x) is the antiderivative of a function ƒ(x) if for all x in the domain of ƒ, http://ptolemy.eecs.berkeley.edu/~celaine/apcalc/topic4.htm

Next: Some Useful Formulas Up: Topics to Study Previous: Differential Calculus Integral Calculus Indefinite Integrals Definition : A function F x ) is the antiderivative x ) if for all x F' x x x dx F x C , where C is a constant. Basic Integration Formulas General and Logarithmic Integrals k x dx k x dx x g x dx x dx g x dx k dx kx C x n dx C n e x dx e x C a x dx C a a x C Trigonometric Integrals sin x dx = -cos x C cos x dx = sin x C sec x dx = tan x C csc x dx = -cot x C sec x tan x dx = sec x C csc x cot x dx = -csc x C tan x dx x C cot x dx x C sec x dx x + tan x C csc x dx x + cot x C Integration by Substitution g x g' x dx F g x C If u g x ), then du g' x dx and u du F u C Integration by Parts u dv uv v du Distance, Velocity, and Acceleration on Earth a t s'' t ) = -32 ft/sec v t s' t s'' t dt dt t C at t v v C C s t v t dt t v dt t v t C Separable Differential Equations It is sometimes possible to separate variables and write a differential equation in the form y dy g x dx = by integrating: y dy g x dx C Exercise Solve for x dx y dy x C Applications to Growth and Decay Often, the rate of change or a variable y is proportional to the variable itself. ky separate the variables k dt integrate both sides y kt C y Ce kt Law of Exponential Growth and Decay Exponential growth when k Exponential decay when k Definition of the Definite Integral a b x dx Properties of Definite Integrals x g x dx x dx g x dx k x dx k dx x dx x dx x dx x dx x dx x dx x g x ) on [ a b ], then

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