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Tag Archives: Integration

Posts on Accumulation

One of the main uses of the definite integral is summed up (pun intended) in the idea of accumulation. When you integrate a rate of change you get the (net) amount of change. This important idea is often treated very lightly, if at all, in textbooks. Here are a series of past posts that use,…

November 19, 2021 in AP Calculus Exams, Integration, Integration Applications.

Unit 8 – Applications of Integration

I haven’t missed Unit 7! This unit seems to fit more logically after the opening unit on integration (Unit 6). The Course and Exam Description (CED) places Unit 7 Differential Equations before Unit 8 probably because the previous unit ended with techniques of antidifferentiation. My guess is that many teachers will teach Unit 8: Applications…

November 16, 2021 in 2019 CED, antidifferentiation, AP Calculus Exams, Integration, Integration Applications.

A Calculus Journey

I think that the path leading up to and including the Fundamental Theorem of Calculus (FTC) is one of the most beautiful walks in mathematics. I have written several posts about it. You will soon be ready to travel that path with your students. (I always try to post on topics shortly before most teachers…

November 9, 2021 in antidifferentiation, Integration, Integration Theory.

The Old Pump

A tank is being filled with water using a pump that is old and slows down as it runs. The table below gives the rate at which the pump pumps at ten-minute intervals. If the tank initially has 570 gallons of water in it, approximately how much water is in the tank after 90 minutes?…

November 5, 2021 in Integration, Integration Applications, Integration Theory.

Unit 6 – Integration and Accumulation of Change

Unit 6 develops the ideas behind integration, the Fundamental Theorem of Calculus, and Accumulation. (CED – 2019 p. 109 – 128). These topics account for about 17 – 20% of questions on the AB exam and 17 – 20% of the BC questions. Topics 6.1 – 6.4 Working up to the FTC Topic 6.1 Exploring…

November 2, 2021 in 2019 CED, antidifferentiation, AP Calculus Exams, Integration, Integration Theory.

Adapting 2021 AB 4 / BC 4

Four of nine. Continuing the series started in the last three posts, this post looks at the AP Calculus 2021 exam question AB 4 / BC 4. The series considers each question with the aim of showing ways to use the question with your class as is, or by adapting and expanding it.  Like most…

July 13, 2021 in AP Calculus Exams, Derivative Applications, Derivative Theory, Graphing, Integration Applications, Integration Theory, Limits, Reviewing.

Applications of Integration – Unit 8

I haven’t missed Unit 7! This unit seems to fit more logically after the opening unit on integration (Unit 6). The Course and Exam Description (CED) places Unit 7 Differential Equations before Unit 8 probably because the previous unit ended with techniques of antidifferentiation. My guess is that many teachers will teach Unit 8: Applications…

November 17, 2020 in 2019 CED, antidifferentiation, AP Calculus Exams, Integration, Integration Applications.

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