Area Between Curves
Definition
The area between curves refers to the region enclosed by two or more curves on a graph. It represents the total space bounded by these curves.
Analogy
Imagine you have two different flavors of ice cream, chocolate and vanilla. The area between curves is like the space inside an ice cream cone where both flavors are mixed together.
Related terms
Functions of x and y: These are mathematical expressions that define how variables x and y relate to each other in a given equation.
Points of Intersection: These are the coordinates where two or more graphs intersect each other on a coordinate plane.
Integration: This is a mathematical process used to find the exact value of the area between curves by summing up infinitely many infinitesimal rectangles.
"Area Between Curves" appears in:
Additional resources (1)
Practice Questions (11)
What are the additional steps required when finding the area between curves that intersect at more than two points?
How do you calculate the area between curves that intersect at more than two points using vertical slices?
How do you calculate the area between curves that intersect at more than two points using horizontal slices?
What is the key step when finding the area between curves that intersect at more than two points?
What should you do after graphing the functions when finding the area between curves that intersect at more than two points?
What is the purpose of integrating from the intersection points when finding the area between curves that intersect at more than two points?
How do you calculate the area between curves that intersect at more than two points using vertical slices when the curves are functions of y?
How do you calculate the area between curves that intersect at more than two points using horizontal slices when the curves are functions of x?
How do you calculate the area between curves that intersect at more than two points using vertical slices when the curves are given in parametric form?
What is the relationship between the area between curves and the integration process?
When finding the area between curves that intersect at more than two points, what is the significance of identifying the intersection points?
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