Find the area, if it exists, of the region between the curve and the x-axis on the given interval. f(x) = 36e¬0.9x x > 4

Q: Find the area under the graph of the function f (x) = xe-* between x 0 and x = 5.

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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.…

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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 – x² and the x-axis.

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Q: Find the area under the region below y = e® and above the x-axis for 0 < x < 2.

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Q: Set up the definite integral required to find the area of the region between the graph of y 19-2 y =…

A: We have to find out area

Q: Find the area under the graph of f(x)= x2 and above the x-axis, between x = 0 and x = 3.

A: Given, f(x) = x2, we have to find the area under the graph f(x) and above x-axis between x = 0 and x…

Q: Find the area between the graph of y and the r-axis for a E [0, b] where b is a (2x2 + 1)2 positive…

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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: (a) Estimate the area under the graph of f(x) = 25 – x from x = 0 to x = 5 using five approximating…

A: Consider the equation as shown below: Here, the function fx =25-x2 And the object is to find the…

Q: Q4. Find the area between curve y = x - 3x + 2 and x-axis from x =0 to x 2

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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: Q1. Find the area under the curve for following equation for the interval (x= 0 to x= 8) 1 y (x- 5)5

A: One of the two main parts of calculus which are concerned with the study of integrals, as opposed to…

Q: Q1. Find the area under the curve for following equation for the interval (x = 0 to x = 8) 1 y (x –…

A: Area under the curve will be given by integrating the function of the curve with respect to x with…

Q: "In Computing the area between two curves, why does f(x) have to be greater than g(x) over the…

A: In computing the area between two curves, why does f(x) have to be greater than g(x) over the…

Q: Find the area between the graph of x = and the y-axis on the interval [1, 4]. 4 3 2- 1 0.5 05 1 1.5…

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Q: Find the area under the graph of f(x)=- e* +e* ,0<xs In3

A: Hi there, At a time we can answer only one question and these all are different questions. These are…

Q: Find the area shown in the graph, bounded by the curves y=0y=0 and y=x2−4xy=x2-4x, for 0≤x≤60≤x≤6.

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Q: Q2/ Find the total area between the curve y = -x² – 2x and the X-axis.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find the area between the graph of y = and the x-axis for x e [0, b] where b is a (2x2 + 1)2…

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Q: Find the area of the region under y = e and above y 1 for 0 < x < 2. =

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Q: Set up the definite integral required to find the area of the region between the graph of y = x² –…

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Q: Find the area under the graph of f(x) = 3x2, above the x-axis, and between x = 0 and x = 2.

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Q: Find the exact area between the curve f (x) = 9 – x², the x-axis, and x=-3 and x=3.

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Q: Find the area under the given curve over the indicated interval. y =x +6x+ 1; [3, 5]

A: To find area under the curve we use definite integrals.

Q: (d) Find the area between the two curves 3 y = x² – 1 1+ x² '

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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&gt;=8

Q: Find the area under the curve between x-2 and x=-1 for the curve f(x)=(7 – x²)d

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Q: Find the area of the region bounded by the y-axis, the line x = 3, and the functions f(x) = 1/2 (x^2…

A: Consider the functions fx=12x2-3x+10 and gx=-13x-1 Find area of region bounded by the y-axis x=0 and…

Q: Q/ A/ Find the area between the curve y 3x- x² and the x-axis

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Q: Find the area of the region between the graphs of y = 15 – x² and y = - 3x + 5 over the interval 0 <…

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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 following methods with n…

A: (a)To approximate the area under the graph of f(x) and above the x axis, using n = 4 and left end…

Q: Find the area bounded by the curve c²y=x³, the x – axis, and the line x =2c.

A: We find the area bounded by the curve using the integration. Before finding the area, first, we will…

Q: Approximate the area under the curve of f (x) = x² +3 from 0 to 4 using the Midpoint Rule with n =…

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Q: Find the total area of the region between the curve and the x-axis 1 xs3 4 ОА. 3 O A. OB. В. О С. 3…

A: *to find:- total area.

Q: Find the area between the curve y = 2(ln x)/x and the x-axis from x = 1 to x = e.

A: According to question, Given curve, y = 2ln xx

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 under the curve y = a²xe¬b²x from x = 0 to x = 5.

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Q: Find the area under the curve y = -over the interval [4, 7]. (3x + 1)2 Enter the exact answer. area…

A: The area under the curve: - Three simple procedures can be used to compute the area under the curve.…

Q: Find the exact area between the curve f (x) = x³, the x-axis, and x=0 and x=4.

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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: 3. Determine the area above f(x) = x² + 2x + 3 and below the line y = 11.

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Q: Solve. 1. Find the area of the region between the function f(x) = 4x + 1 and the x– axis on the…

A: Note :As per our guidelines we are supposed to answer only one question if there are multiple…

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: 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: approximate the area under the graph of f(x) and above the x-axis using the following methods with n…

A: Ypu have asked a question with four sub parts. I have answered the first three sub parts. Please…

Q: The area under the curve y =3/x over the interval [1.4]is equal to: 14

A:

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.