AP Calculus AB · Unit 8: Applications of Integration
8.5 Finding the Area Between Curves Expressed as Functions of y
In short
You are expected to calculate areas of regions in the plane using definite integrals where the bounding curves are expressed as functions of y. This builds on the enduring understanding that definite integrals allow us to solve problems involving the accumulation of change in area over an interval.
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What else do you need to know about Finding the Area Between Curves Expressed as Functions of y?
The focus is specifically on setting up and evaluating integrals with respect to y.
Can you do these?
- I can calculate the area of a region in the plane by setting up and evaluating a definite integral with respect to y.
How is Finding the Area Between Curves Expressed as Functions of y tested on the exam?
On the AP Exam, you must be able to determine whether the 'thickness' of a region is with respect to x or y based on the orientation of the curves. You should practice solving variations on calculus-based geometry problems until you can decide which variable to integrate with respect to without prompting. In free-response questions, you are required to show supporting work by presenting a correct expression using appropriate notation and the mathematical structures of solutions.
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Finding the Area Between Curves Expressed as Functions of y: common questions
What do you need to know about Finding the Area Between Curves Expressed as Functions of y for AP Calculus AB?
You are expected to calculate areas of regions in the plane using definite integrals where the bounding curves are expressed as functions of y. This builds on the enduring understanding that definite integrals allow us to solve problems involving the accumulation of change in area over an interval.
How is Finding the Area Between Curves Expressed as Functions of y tested on the AP Calculus AB exam?
On the AP Exam, you must be able to determine whether the 'thickness' of a region is with respect to x or y based on the orientation of the curves.
How do I know I have mastered Finding the Area Between Curves Expressed as Functions of y?
Check you can do each of these: calculate the area of a region in the plane by setting up and evaluating a definite integral with respect to y.
Where does Finding the Area Between Curves Expressed as Functions of y fit in AP Calculus AB?
Finding the Area Between Curves Expressed as Functions of y is topic 8.5 in Unit 8: Applications of Integration of AP Calculus AB.
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