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# CALC ANALYT GEOM II MATH 125

UW

GPA 3.76

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This 2 page Study Guide was uploaded by Addison Beer on Wednesday September 9, 2015. The Study Guide belongs to MATH 125 at University of Washington taught by Staff in Fall. Since its upload, it has received 22 views. For similar materials see /class/192084/math-125-university-of-washington in Mathematics (M) at University of Washington.

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Date Created: 09/09/15

MATH 125 EXAM 1 REVIEW Exam 1 will cover 410 51 55 and 61 63 This review sheet discuss in a very basic way the key concepts from these sections This review is not meant to be all inclusive but hopefully it helps you remember basics Please notify me if you find any typos on this review sheet If you understand the concepts behind all the homework problem and if you can complete them quickly and completely then you will do well on the exam The exam will test you on the same concepts and ideas as the homework problems 1 A Chronological Review 0 Section 410 Know how to find antiderivatives Understand the significance of C Understand how to find distance from velocity and velocity from accelera tion by using antidifferentiation and initial values Section 51 52 Understand the development of the Reimann integral and the de finition of the definite integral bfzdz lim a naoo i1 Be comfortable with this right hand side and how to interpret the part 2 f Az as the sum of approximating rectangles In conjunction with these ideas you should know how to approximate an integral by using 71 rectangles and either left endpoints right endpoints or midpoints 0 Section 53 The Fundamental Theorem of Calculus FTOC Know parts 1 and 2 By now you should understand the importance of the FTOC Part1 If gz f ftdt then gz m Part 2 If F is any antiderivative of f that is F f z then Ab mm Fb 7 Fa Part 1 gave us a derivative rule for integral functions with variables as endpoints You should how and why to use the chain rule and how and when to break up the integral into two parts Part 2 is used in evaluating definite integrals It is vital that you understand both of these parts 0 Section 54 The indefinite integral was defined as the general antiderivative and use the following notation f zdz the general antiderivative of f don39t forget C 39 You should memorize all the basic integrals lncluding f z dz f dz f 5 dz fsinz dz foosz dz se02z dz fos02z dz foscz cotz dz andfsecz tanz dz You should also know from Calculus l f 21 dz and from class f tanz dz 1 Section 55 Here we introduce the first major integral techniques Know how to set up and use the u substitution template as described in class You should know how to choose your u effectively and efficiently l have stressed this material in class and via practice sheets online you should know this well Section 61 Understand how to find the area between two curves In particular you should be able to draw a typical rectangle39 and you should be able to decide if z or y is a better choice 17 Using dz TOP 7 BOTTOM dz 1 Using dy RIGHT 7 LEFT dy Section 62 Understand how to find volumes using the method of slicing You should be able to draw a typical slice by cutting across the axis of rotation 17 Volume 2 Area Formula for a Typical Slice dz or dy For solids of revolution the slices are typically disks Area 7rradius2 or washers Area 7router radius2 7rinner radius2 0 Section 63 Understand how to find volumes using the method of cylindrical shells You should be able to draw a typical shell and don39t forget to label the radius as z or y 17 Volume 2 Surface Area Formula For a Typical Shell dz or dy 17 Volume 2 27TRadius FormulaHeight Formula dz or dy Using either of these methods takes practice there is plenty of problems to practice on in your book 2 Miscellaneous 0 One interpretation of the integral was the integral of a rate of change of a quantity gives the net change in that quantity39 a Big Example 5 vtdt 5b 7 5a We used this to answer questions about falling tomatoes39 and falling rocks39 We also discussed particles moving on a straight line You should know how to answer questions about displacement39 and total distance traveled39 0 You should know what Ln Rn and Mn represent as approximations to integrals and how to compute them even if you don39t have a picture

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