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Area between curves with ✌️MULTIPLE✌️ INTERSECTIONS?!! 🤯🤯 #apcalculus #apcalc #unit8 #shorts
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We explore the process of finding the area between two curves that intersect at multiple points, which presents a unique challenge in calculus, as the relationship between the curves changes across the interval.
The first method we discuss involves dividing the area into multiple segments, one for each interval between intersections. This approach ensures that we always subtract the lower curve from the upper curve within each segment, requiring separate integrals for each section where the curves' relationship changes. The second method offers a more unified approach, allowing us to calculate the area in one step by integrating the absolute value of the difference between the functions, over the entire interval, which simplifies the process by not requiring separate calculations for each segment, yet it accurately accounts for the change in which function is on top.
Both methods yield the same result for the area between the curves, providing flexibility in how the problem can be approached.
#APCalculus #AreaBetweenCurves #CalculusTutorial #MathConcepts #IntegrationMethods
Unit 8 of AP Calculus is all about Applications of Integration:
8.1 Finding the Average Value of a Function on an Interval
8.2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals
8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts
8.4 Finding the Area Between Curves Expressed as Functions of x
8.5 Finding the Area Between Curves Expressed as Functions of y
8.6 Finding the Area Between Curves That Intersect at More Than Two Points
8.7 Volumes with Cross Sections: Squares and Rectangles
8.8 Volumes with Cross Sections: Triangles and Semicircles
8.9 Volume with Disc Method: Revolving Around the x- or y-Axis
8.10 Volume with Disc Method: Revolving Around Other Axes
8.11 Volume with Washer Method: Revolving Around the x- or y-Axis
8.12 Volume with Washer Method: Revolving Around Other Axes
8.13 The Arc Length of a Smooth, Planar Curve and Distance Traveled (BC only)
_____
For extra help with your AP Calc (AB or BC), get my Ultimate Review Packet to help you review all year long and get prepared for the AP test:
The first method we discuss involves dividing the area into multiple segments, one for each interval between intersections. This approach ensures that we always subtract the lower curve from the upper curve within each segment, requiring separate integrals for each section where the curves' relationship changes. The second method offers a more unified approach, allowing us to calculate the area in one step by integrating the absolute value of the difference between the functions, over the entire interval, which simplifies the process by not requiring separate calculations for each segment, yet it accurately accounts for the change in which function is on top.
Both methods yield the same result for the area between the curves, providing flexibility in how the problem can be approached.
#APCalculus #AreaBetweenCurves #CalculusTutorial #MathConcepts #IntegrationMethods
Unit 8 of AP Calculus is all about Applications of Integration:
8.1 Finding the Average Value of a Function on an Interval
8.2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals
8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts
8.4 Finding the Area Between Curves Expressed as Functions of x
8.5 Finding the Area Between Curves Expressed as Functions of y
8.6 Finding the Area Between Curves That Intersect at More Than Two Points
8.7 Volumes with Cross Sections: Squares and Rectangles
8.8 Volumes with Cross Sections: Triangles and Semicircles
8.9 Volume with Disc Method: Revolving Around the x- or y-Axis
8.10 Volume with Disc Method: Revolving Around Other Axes
8.11 Volume with Washer Method: Revolving Around the x- or y-Axis
8.12 Volume with Washer Method: Revolving Around Other Axes
8.13 The Arc Length of a Smooth, Planar Curve and Distance Traveled (BC only)
_____
For extra help with your AP Calc (AB or BC), get my Ultimate Review Packet to help you review all year long and get prepared for the AP test:
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