Consider a graph of f(x)=x3−2x2+2 and f(x)=x. Find the area of the region bounded between the curves on [−1,2].

Q: Find the total area between the curve of the function f(x)=x−2 and the x-axis over the interval…

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Q: (1) Sketch the graphs y = x¹(x+2) and y = x(x+2) for the domain [-2, 1] shading the areas between…

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Q: Find the area below the curve f(x) = √√4-x4 2x from x = 0 to x = √√2

A: The objective of this question is to find the area under the curve defined by the function f(x) =…

Q: 8. Given, h(x) =2 – x and g(x) = -x² + 4 a) Plot the two functions on the same graph for -2 < x <4…

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Q: 2. f(x) = -2x2 -8x-3 -2 Vertex: AOS: Min / Max: y-int.: Domain: Range:

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Q: Calculate the area confined by between the portion of the graph of the function f(x) = -(x – 2)² + 4…

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Q: Determine the area, in square units, bounded above by f(x)=−x^2−10x−16 and g(x)=2x+16 and bounded…

A: Given that fx=-x2-10x-16gx=2x + 16 The objective is to find the area of the region which is bounded…

Q: What is the area between the graphs of f (x) = 3x + 5, g(x) = -2x – 3, x = 2, and x = 12?

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.