area between 2 curves
The area between two curves refers to the region bounded by two graphs on a coordinate plane
The area between two curves refers to the region bounded by two graphs on a coordinate plane. To find the area between two curves, follow these steps:
1. Identify the two curves: Let’s call them f(x) and g(x), where f(x) represents the upper curve and g(x) represents the lower curve.
2. Determine the intersection points: Set f(x) equal to g(x) and solve for x to find the x-values where the two curves intersect. These intersection points will be the boundaries of the region.
3. Evaluate the definite integral: Integrate the difference between f(x) and g(x) with respect to x over the interval between the x-values of the intersection points. This will provide the area between the curves.
Mathematically, the area between two curves can be calculated using the following definite integral:
Area = ∫[a, b] (f(x) – g(x)) dx
where ‘a’ and ‘b’ are the x-coordinates of the intersection points.
It’s important to take note of the absolute values or apply appropriate adjustments if the curves cross each other multiple times within the interval of interest. Also, consider negative areas below the x-axis as they contribute to the total area.
Remember to simplify the integral if possible and perform any necessary calculations to determine the area between the curves accurately.
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