Find the area of the region bounded by the graphs of the given equations. y=4-x^2, y=4-4 x

Name: Problem 33, Chapter 4: Calculus and Its Applications
Uploaded: 2020-10-25T15:14:50-08:00
Duration: 5 min 37 s
Channel: Ahmad Reda
Description: Find the area of the region bounded by the graphs of the given equations. y=4-x^2, y=4-4 x

step 1 In program 33 we want to get the area enclosed between these two graphs the parabola and the lin

Find the area of the region bounded by the graphs of the...

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Key Concepts

Solving Quadratic Equations

Problems that involve a quadratic function and a linear function often require solving a quadratic equation to find the points of intersection. These solutions are crucial, as they determine the bounds for the integration used in calculating the area.

Definite Integration

Definite integration is used to compute the exact area under a curve within given limits. In the context of finding areas between curves, the definite integral accumulates the area differences over the interval between the intersection points.

Intersection of Graphs

When finding the area between curves, the first key step is determining where the graphs intersect. These intersection points provide the limits of integration and define the region over which the area is calculated.

Area Between Curves

The area bounded by two curves is determined by integrating the vertical distance between the top curve and the bottom curve over the interval defined by their intersection points. This method subtracts the lower function from the upper function to find the net area.

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