The area between the curve y = = and the x-axis from x = 10 to x = 20 is the same as the area between the curve and the x-axis from x 1 to x = 2.

Q: Find the area between the curve y = x² + 8x + 12 and the x-axis from x = -2 to x = 0. (Give an exact…

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Q: Find the exact area between f(x) = 2x and g(x) = 15 – x from the vertical axis to their point of…

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Q: How many individual areas in the total area bounded by the curve y=x - 3x +2x and by the x-axis from…

A: first we plot the given region then decide how many areas exist

Q: Find the value of Z such that the proportion of the area. 2. To the right of Z-score is 0.5500 3. To…

A: We have given that the proportion of the area.

Q: Find the area below the x-axis and bounded by the curve  y=1-2x for 5<=x<=7.

A: The given curve is: y = 1 - 2x;  where 5 &lt;= x &lt;= 7 The graph is as follows:

Q: Find the area between the curve y = -x< + 6x – 8 and the x-axis from x = 2 to x = 4. (Give an exact…

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Q: Find the area bounded by the line f(x) equals 3X -1, the curve G(x) equals X^2-6X +7 , and the two…

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Q: Find the area enclosed by the two curves  f(x)=3xe3x  and g(x)=5x between x = 0 nad x = 1 Give…

A: The given functions are: f(x)=3xe3x      and      g(x)=5x The given function intersect at:  x=13ln53

Q: Find the area between the curves. y = x2 − 2x + 7 and y = x2 + 8 from x = 0 to x=6

A: Let fx=y=x2-2x+7 and gx=y=x2+8. First, we will find the intersection point of both the curves…

Q: Find the area of the region bounded by the curve f(x) = ex -3 and the x-axis , and between x = 0 and…

A: The region bounded by the curve f(x) = ex -3 and the x-axis , and between x = 0 and x = 2 is as…

Q: What is the area under the curve of the following positive function y = 10x4 + 3x² between x = -1…

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Q: The area between y= 2sinx and y = sin2x for 0<x ST is

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Q: The area between y = n + x* and the x- axis in the interval [0, 1] approximated using left endpoint…

A: Find your answer below

Q: The sum that best approximates the area under the curve between the function and x-axis on the…

A: our objective is to find the best approximation

Q: Solve for the area beneath the curve y = -(x – 1)² + 10 and above the axis from x = -1 and x = 2.

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Q: evaluate the definity integral  from -10 to 10  (2 - x)dx

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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: b) Find the area between the 2 curves f(x)=x²+4-4x and x-axes and border with the two lines = 5 &x=…

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Q: The area under flx) between X=L and x=2 fal= 3x2

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Q: Find the area between the graph of y = 3x2 + x and the x-axis for x=0 to x=1. %3D

A: From the given curve the bounded region is shown below:     Now using the double integral method to…

Q: Find the area between the curves y = cos(x) and y = sin(x)  from x = -3π/4 to x = π/4. Draw the…

A: To find the area between the curves.

Q: The area under the curve y = cos x from x = a to x = is 0.2. What is the value of a 2 rounded to…

A: Area under a curve y(x) is given by ∫abydx         where a≤x≤b

Q: Find the area between y = (x - 2)ex and the x-­axis from x = 2 to x = 4.

A: The area between y = (x - 2)ex and the x-­axis from x = 2 to x = 4 is given as: Area=∫24x-2exdx To…

Q: The area under the curve y = 2x bounded from below bythe x-axis and on the right by x = 4 is 16 3…

A: Given that the area under the curve y=2xwe need find the area below the x-axis and the right by x=4

Q: Find the area of the “triangular” region in the first quadrant that is bounded above by the curve y…

A: Consider the provided curve,  Bounded above by the curve y=ex2 and below by the curve y=e-x2. And on…

Q: the area between the curves x^(2) and x^(4)

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Q: 1. Sketch a region bounded by the function ƒ (x)= x+1 the x axis and two vertical lines so that the…

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Find the area under the curve f(x) =x+3x+7, above the X axis from x=4 to x=6.

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Q: Find the area of the surface formed by revolving g(x) = x^3 on the interval [0, 1] about the x-axis.…

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Q: 2. Find the total area under the curve f(x) = 2xe² from x = 0 and x = 5.

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Q: Find the area between the curve ​f(x)=x^2​+15 and the​ x-axis from x=3 to x=5.

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

Q: Find the exact area below the curve y = x°(1 – x) and above the x-ax is. %3D

A: y=x31-x Diagrammatic representation of the required area is,

Q: Find the area bounded by the function f(x) equals .3x^3-1.5x^2+19 the X axis and the lines X=2 and…

A: We will find out the area under the curve.

Q: Find the areas between the curves y = 2(log2 x)/x and y = 2(log4 x)/x and the x-axis from x = 1 to x…

A: To determine the area between the curves and the x-axis.

Q: Approximate the area under the curve graphed below from 3 to x = 6 using a Left Endpoint…

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Q: The area between y 3 x + 1 and y x2 from x = 1 to x 3 is

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Q: Find the area bounded by y=-17(x2 - x - 12) and the x-axis. Answer in two decimal places.

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Q: Find the area between the curve y = x2 + 10x + 24 and the x-axis from x = −4 to x = −1.

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Q: 4. Find the area under the curve y = Vx +6 from x = -6 to x = 3. Give exact answer.

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Q: Find the area under the curve y 5 -over the interval [4, 7]. (3x + 1)² Enter the exact answer. area…

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Q: Find the area under the curve 4x2-3x+6 between x= -2 and x=3

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Q: Find the area under the curve over the indicated interval. [4.3] y = 4 – x²; [-2,1] y = x + 2x + 1;…

A: Please refer the attached image for complete solution.

Q: Find the area between the curve y - x + 9x + 20 and the x-axis from x - -4 to x - -2. (Give an exact…

A: Given, y = x2 + 9x + 20  x = -4 and x = -2  We have to find the area of between the curve y = x2 +…

Q: 3. Find the area between the curve y = 2sinx cos x and the x-axis within the interval [0,2π].

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Q: Approximate the area under the curve y=1/x from x=1 to x=4 using the left endpoint estimate with six…

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

Q: Find the most general antiderivative or indefinite integral. 8/x dx

A: We have to find the indefinite integral.

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

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Q: 4 Find the area bounded by the curve y = the x - axis, and the vertical lines x = -2 x²+4 and x = 2.

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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.