AP Calculus AB · Unit 8: Applications of Integration
8.6 Finding the Area Between Curves That Intersect at More Than Two Points
In short
You must be able to find the area of regions bounded by curves that intersect at more than two points. This requires determining all points of intersection to establish the bounds of integration and splitting the region into sub-intervals where the upper and lower curves do not change.
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Can you do these?
- I can calculate the area between curves that intersect at more than two points by using a sum of definite integrals or the absolute value of their difference.
How is Finding the Area Between Curves That Intersect at More Than Two Points tested on the exam?
You may be assessed on your ability to identify all points of intersection, set up the appropriate integral(s), and evaluate them either by hand or using a graphing calculator. In free-response questions, you must show supporting work by presenting a correct expression using appropriate mathematical notation. A common pitfall is failing to split the integral at intersection points, which can be avoided by graphing the functions or using the absolute value of their difference.
Free practice questions with full explanations, and instant marking of your free-response answers.
Finding the Area Between Curves That Intersect at More Than Two Points: common questions
What do you need to know about Finding the Area Between Curves That Intersect at More Than Two Points for AP Calculus AB?
You must be able to find the area of regions bounded by curves that intersect at more than two points. This requires determining all points of intersection to establish the bounds of integration and splitting the region into sub-intervals where the upper and lower curves do not change.
How is Finding the Area Between Curves That Intersect at More Than Two Points tested on the AP Calculus AB exam?
You may be assessed on your ability to identify all points of intersection, set up the appropriate integral(s), and evaluate them either by hand or using a graphing calculator. In free-response questions, you must show supporting work by presenting a correct expression using appropriate mathematical notation.
How do I know I have mastered Finding the Area Between Curves That Intersect at More Than Two Points?
Check you can do each of these: calculate the area between curves that intersect at more than two points by using a sum of definite integrals or the absolute value of their difference.
Where does Finding the Area Between Curves That Intersect at More Than Two Points fit in AP Calculus AB?
Finding the Area Between Curves That Intersect at More Than Two Points is topic 8.6 in Unit 8: Applications of Integration of AP Calculus AB.
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