f(x) = for (-x, 1] (x – 2)2*

Q: Find the area, if it exists, of the region between the curve and the x-axis on the given interval.…

A:

Q: 1. Determine the area below f (x) = 3+ 2x – x² and above the x-axis.

A: 'Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the area between the graph of the given function and the x-axis over the given interval, if…

A: ∫x1+x22 dx Put  1+x2=t⇒0+2x=dtdx⇒2x dx=dt⇒x dx=dt2 Therefore, ∫x1+x22 dx=∫dt2t2=12∫t-2…

Q: 1. Find the area in the first quadrant bounded by f(x)=4x-x^2 and the x-axis. f(x) = 4x-x² 3 2 3 1 2…

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Q: Let A be the area of the region that lies under the graph of f(x) =e -x  between x =0 and x =2

A: The diagrammatic representation of the area is,

Q: Calculate the area, in square units, bounded above by f(x)=x2+4x+4 and g(x)=−4x+4 and bounded below…

A: Consider the curves, fx=x2+4x+4,   gx=-4x+4 To sketch the graph: Here there are two region be…

Q: Find the area between the graph of the function and the x-axis over the given interval, if possible.…

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Q: Determine the expression for the area under the curve f(x) on the closed interval [0, 3] with n…

A: Definition of the definite Integral

Q: Find the area between f(x)=x²-7 and the x-axis from x = 0 and x = 6. ...

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Q: Find the total area between the graph of f(x)=x2−5 and the​ x-axis from x=0 to x=6.

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Q: Let f (x) = |x³ + 125| Find the area A of the region between the graph of f and the x axis on the…

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Q: Find the area under the graph of y = x² + l over the interval [-1, 2]. In this case, f(x) = x² + 1,…

A: area of graph within limits given by integrating function within limits

Q: Find the area of the region between the curve and the x-axis. In 4 3x f(x) = e - 4 from 0 to 3

A: By using area formula, we calculate the required area of the region.

Q: Find the area between the graph of f (x) = x² – 2x and the x-axis from x = -1 to x =

A:

Q: Let f (x) = |x³ + 216|| Find the area A of the region between the graph of f and the x axis on the…

A: Let the function given is  f(x)=|x3+216|

Q: find the area between f(x)=x2+2 and g(x)=-x+1 on [1,3]

A: Draw the graph. To find the region between the red and blue function: Red: y=x2+2 Blue: y=-x+1…

Q: Find the area enclosed between f(x )= 0.8x^2 + 9 and g(x) = x from x = −2 to x = 4

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Q: Find the area between the graphs of the given functions f(x) =x+2, and g(x) =x' -4

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Q: Find the area, if it exists, of the region between the curve and the x-axis on the given interval.…

A:

Q: Find the area, if it exists, of the region under the curve on the given interval of the x-axis. f(x)…

A: Given. Y = e-3x Area is  dA = e-3xdx Interval is  X>=8

Q: Find the area of f(x) = 3 +2x – x² above the x-axis.

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Q: Draw the graphs and find the between the area curves f(x) = (-1)*x² +(-1)°(c+3)x+(-1)*(a+2) and…

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Q: If f(x) is a strictly increasing continuous function with domain [0, 00]. If f3(x) = tf()dt. 0, Find…

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Q: Find the total area between the curve of the function f(x)=2x+4 and the x-axis over the interval…

A: We have to find the total area under f(x)=2x+4 and the x-axis over the interval [−9,−1]Recall that…

Q: Let f (x) = 8/x^2  . Compute the area A of the region between the graph of f and the x axis on the…

A: Given: f(x)=8x2interval[−7,−4]

Q: approximate the area under the graph of f(x) and above the x-axis using the left, right, and…

A: f(x) = 3x + 2 from  x=1  to  x=3; n = 4dx = Width of each rectangle = (3 - 1) / n = 2 /4 = 0.50

Q: Let f (x) = |x3 + 216| Find the area A of the region between the graph of f and the x axis on the…

A: given area can be found as below :

Q: 3. Find the area between the graph of f (x) = x² – 2x and the x-axis from x = -1 to x = 1

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Q: 1. Find the area in the first quadrant bounded by f (x) = 4x- x and the x-axis.

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: find the area between f(x)=x^2-16 and the x axis from x=0 to x-=9

A: The given function is fx=x2-16 We have to find the area between fx and the x-axis from x=0 to x=9

Q: Estimate the area between the x-axis and the graph of f(x) = 9 – 2° over the interval [0, 3] by…

A: Given function is f(x)=9-x2 we have to find the area over interval [0, 3]. Since there is 3…

Q: Find the area between the curves f(x) = x2+2x+1 and g(x) = x+1

A: We need to find area between given curves.

Q: (1) Find the area enclosed by the two functions f(x) = x² – 1, and g(x) : -x4 + 1.

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Q: Find the area between the curves f(x) and g(x) 2. f(x) = 3x, g(x) = x² – 3x + 8

A: We will find the area between the two curves.

Q: (Area Under a Curve)

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Q: b) Find the area enclosed between f(x)= = -x² + 4x and g(x) = x² - 6x + 5, over the interval 0≤x≤ 1.

A: Sol

Q: Find the area, in square units, bounded above by f(x)=x2+8x+16 and g(x)=x+10 and bounded below by…

A: The given functions are fx=x2+8x+16 and gx=x+10 .

Q: Find the area under the graph of f(x) = r² + 5 between x = 0 and = 6. %3D

A: The function is given by fx = x2+5 To evaluate: The area under the graph of the function fx between…

Q: Calculate the area between the graph of f(x) = x² (x + 4) and the x-axis given x E [0, 5].

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Q: For F(x)= 3+3x-2x^2 A. Sketch the graph and the rectangles from x=0 to x=2 using n=4 and right…

A: The given function is:…

Q: 4. Find the surface area of the function x when revolved around the x-axis. between x=0 and x1

A: When a curve is revolved about an axis, we obtain a surface and there are several pre-defined…

Q: Which of the following represents the area bounded by the graphs of f(x) = −x3 + 12x and g(x) = x2

A: Definition used-       The area between two curves f(x) and g(x) is given by -             A…

Q: Find the area between f(x) = x - 1 and g(x) = -x² + 6x - 5 %3D

A: We have been given the graphs f(x)=x-1g(x)=-x2+6x-5

Q: Find the area, if it exists, of the region under the curve on the given interval of the x-axis. 1…

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Q: 9) Given the function f(x)=-3x+2 , find the net signed x-axis over the interval [-5,3]. area between…

A: Given function is  f(x)=-3x+2 We have to find the area of the region bounded by the given function…

Q: Consider the region bounded above by g(x)=−9x−9 and below by f(x)=x2 −9x−18. Find the area, in…

A: Calculation:The given curves are f(x) = – 9 x – 9 and g(x) = x2 – 9x – 18.The area enclosed by two…

Q: Find the area between  F(x) = x^2-5 and the x-axis from x=0 and x=9

A: Given query is to find the area under the curve.

Q: Find the area between the curves f(x) = x^2 - 4x +12 and g(x) = x^2 - 2x + 2  for 0 ≤ x ≤ 3

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Q: Estimate the area between the x-axis and the graph of f(x) = 9 – x over the interval 0, 3 by using…

A: The given function f(x)=9-x2 over the interval [0,3]

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.