Find the area bounded by the ff. curves and lines: a. y = xe^–x , the x-axis and the maximum ordinate.

Q: By integration, determine the area bounded by the curves y = 6x – x ^2and y = x^2 – 2x.

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Q: Find the area bounded by tHe curves y=8x-x and y= 3x

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Q: Calculate the total area of the region bounded by the line y= 6x^2 + 9, the x-axis and the line x =4…

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Q: Determine the area bounded by the curves y=sinhx, y=coshx, the y-axis and the line y=1.

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Q: Find the area between the curves.

A: First sketch the region bounded by the curves x=1,  x=6,  y=1x  and  y=12 as shown below.

Q: Find the area between the curves. x = -3, x = 0, y = 1 -x2, y = 0

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Q: Find the area bounded by the indicated curves. y = x4 - 18x? + 81, y = 81 - x

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Q: A curve is such that the area bounded between the curve, the y-axis, the x-axis and the line…

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Q: Calculate the area of the segment cut from the curve y = x(3 – x) by the line y = x.

A: here we have to find the area of the region bounded by the curve and line.

Q: Find the area bounded by the curve: y = 8x – x² and y = 3x

A: a) Consider

Q: Find the area of the region in the first quadrant bounded by the line y=3​x, the line x=4​, the…

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Q: What is the area of the region between the graps y = x – 1 and line y = -x – 1

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Q: Find the area enclosed between the curve y = 9 - x squared and line y = x + 7

A: This question is based on application of integration.

Q: What is the area bounded by the curves y2= 6x and x2 = 6y?

A: topic - area bounded by curves

Q: Find the area bounded by the curve y=x^2 − 4, the lines y = 0 and x = 4

A: The graph is shown below:

Q: FIND THE AREA BOUNDED BY THE PARABOLA x = 8+2y-y², THE Y-AXIS, AND THE LINES y = -) AND y = 3

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Q: Find the area of the region bounded by the curve y = 9 - x2 and the x-axis.

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Q: Determine the area bounded by the curves y = -x² – 16x + 36 and y = (x – 2)².

A: Answer

Q: Find the area bounded by the curve y²=9x and its latus rectum

A: Given equation is y2=9x the equation of parabola is of the form  y2=4axlatus rectum x=a  and…

Q: Determine the area bounded by the curves x³ - y = 0 and y + 3x² - 4 = 0, using a vertical element.

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Q: Find the area under the curve y = 3xe for æ > 3. area =

A: Given:The given curve is y=3xe-x and x≥3To find:we have to find the area under the curve

Q: y = 4 – x2 y = 4 – 4x - -5-

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

Q: Find area enclosed by curves y=2x, y=4x^2

A: Area enclosed by two curves is the measure of the area occupied by their intersection.

Q: Find the area bounded by the curve y = 3x – x3 and the line y = 2

A: Given: y= 3x-x3; y=2 If f(x)> g(x) in the interval x=a to x=b, then the area between two curves…

Q: Find the area bounded by the curve y = 9 – x2 and the x-axis.

A: Area

Q: find the area bounded by the given curves y=8x3+7 and y=8x+7

A: Given,           The curves are y=8x3+7 and y=8x+7.

Q: Determine the area bounded by the curve y = 2x - x^2 + 5 and the line joining the points (3,2) and…

A: Please see the explanation below

Q: Find the area between the curves. x = -2, x = 1, y = 2x2 + 5, y = 0

A: Given, x=-2,x=1,y=2x2+5,y=0

Q: ded by the curve or line: y2+4x-8=0, Y

A: Given that: The equation of the curve y2 + 4x - 8 = 0. The equation of the line y = 2x.

Q: Find the area between the curves. x = -5, x=2, y = 3x, y = x² - 4

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Q: The area bounded by the curve y^2 = 12x and the line x = 3 is revolved about the line x =3. What is…

A: Recall: Formula for volume,    V=π∫ab(radius)2dy Given,  y2=12x Substitute x=3 in the above…

Q: Find the area on the first quadrant bounded by the curve y = 2Vx and the lines y = 1,x = 4 and the…

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Q: Find the area of the region between the curves 4x + y = 12 and x = y. Area between curves

A: Solution

Q: Find the enclosed area by the curve with equation y=x^2-9 and x-axis in the region[-1,2]

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Q: Find the area between the curves.    x = - 5, x = 1, y = 10 x, y= x 2 -11

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Q: Find the area bounded by the given curves. y = 8x' + 3 and y = 8x + 3 square units

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Q: What is the area bounded by the curves y=x2+5 and y=−x2, the line x=3, and the y axis.

A: Given that, The curves are y=x2+5 and y=-x2, the line x=3, and the y-axis. Find the area bounded by…

Q: Find the area between the curves y = 4x° and y= 3x + 1.

A: Given the curves y=4x2 and curve y=3x+1. We need to find the area between two curves.

Q: y = 2x ,2 y+ 4x – 8 = 0

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Q: y=9-x2 and ミ-4

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Q: Find the area between the curves. y=x² - 23, y = 9 – 4x

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Q: Determine the area bounded by the curves y = -r - 18z + 40 and y = (x- 2)2.

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Q: Find the area bounded by the curves y = x(x − 1)², y — axis, and the line y = 12.

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Q: Find the area of the region between the curves 4x + y = 12 and x = y. Area between curves =

A: R

Q: Determine the area bounded by the parabola y = x^2, the line y = 6-x, and the x-axis

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Q: Calculate the total area of the region described. Do not count area beneath the x-axis as negative.…

A: Topic = Application of integration

Q: Find the area bounded by the curves y=ex+2, y-axis, y=1, and the line x=3

A: Find the area bounded by the curves y=ex+2 and y-axis, i.e., x=0, y=1, and the line x=3. Limit for x…

Q: find the area of the region bounded by the curve y=x2 - 4x+3  , x axis and the lines x=2 and x=4

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Q: Find the area of the region bounded by the curve y=1--x2 and the x-axis. 9

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Q: Find the area bounded by the curve or line: 4y = x2-2lnx, y=0, x=1, x=4

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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.