Using vertical element, find the area bounded by the curve y2 = 8(x − 4), the line y = 4, y-axis, and the x-axis.

Q: Find the area bounded by the following curves. y=8-x, y 8x-x, x=0, x=2 The area is

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Q: Find the area bounded by the curve y = - -x³x²+3x and the line y=x. 16 4 (A) 10 square units B 8…

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Q: Find the area of the specified region. (Do not count area below the x-axis as negative.) the area…

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Q: Sketch the curve, y=-x +9. Then, find the area between the curve and the x- - axis over the…

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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: What is the area of the region enclosed by the curve y=e^x and the lines x=-1 and y=3?

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Q: Estimate the area of the curve y = 2x + x - 3 from x = 1 to x = 3 by using 5 rectangles and right…

A: We have the lower limit, a = 1, and the upper limit, b = 3.  We are using five rectangles, that is n…

Q: Find the area between the curves x = y-1 and x =

A: Given:- x=y2 -1, x =2y2 -2 To find:- Area between given curves

Q: Find the area of the region bounded by the curve y=1– x2 and the x-axis. - 4 square units 6 square…

A: Solved below

Q: Find the area bounded by the curve y=4x-x? and the lines x=-2 and y=4.

A: The given equation forms a downward parabola.

Q: The total area bounded by the graph of y = r- 1 and the x-axis is represented by 2.

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Q: Find the area bounded by the curve y = 8 – x and both coordinate axes in the first quadrant. Area of…

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Q: Find the total area between y = 25 - x² and the x-axis for 0 < x≤ 6. Area

A: Given is the curve y=25-x2. The objective is to find the total area between this curve and x axis.…

Q: Determine the area enclosed by the curve y=5x2+2, thex-axis and the ordinates x=0 and x=3. Find also…

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Q: The area bounded by the x-axis and the parabola y = 6 - x - x?

A: The solution is given as

Q: Find the area between the curve y = x2 + 9x + 14 and the x-axis from x = −2 to x = 0. (Give an exact…

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Q: by the x-axis (y = 0)

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Q: Find the area between the curves. x= - 2, x = 2, y =7x, y=x² - 8 The area between the curves is

A: Given,           x = -2,  x = 2,  y = 7x  and  y = x2 - 8

Q: The area bounded by the curve y2=12x and the line x=3 is revolved about the line x=3. What is the…

A: The correct answer is option C. Given  y2=12x and equation of line x=3 The point at which the line…

Q: Q3 Answer with all details, find the area of region in the first quadrant bounded on the left by the…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Find the area :  The curve y=4x-x2 and the lines y=0, x=1 and x=3.

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Q: Find the area of the region bounded by the curve y=x²-1 and the line y = 24! The area is

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

A: Given, We have to find the area enclosed by the x-axis and the curve y=-x2+9.

Q: Find the area of the region between the x-axis and the curve y = 8/(x² −4) for x ≥ 4.

A: Integrals and derivatives are considered as the inverses of each other. For example if we have a…

Q: area of the curve: x=y^2+8 ;x

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Q: Find the area between the curves y = 3  x and y = x2 9:

A: Given curves are, y=3x and y=9x2.

Q: Find the area under the curve  y= (2x2 - 7) / (sqrt(x)) ,   16 <= x <= 20

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Q: Find the area of the specified region. (Do not count area below the x-axis as negative.) the area…

A: The area is bounded by the curves:y=25-x2 ; x axis ; x=-5 and x=5

Q: Find area of the region under the curve y = 3x³ – 5 and above the xt-axis, for 2 < x < 5. area =

A: Graph of the equation:

Q: Find the area of the region bounded by the graphs of y = (square root (x)) and y = x/2. Leave the…

A: Find the area of the region bounded by the graphs of y=x and y =x2

Q: The total area bounded by the graph of y = 5 - x, the line a x = 0 and the x-axis

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Q: Find the area bounded by the given curves. y = x2 − 1 and y = 8 − 8x2        square units

A: Given :

Q: Solve the area bounded by y³+10 = x², the lines y=-2 and y=2 *

A: Here is the solution of the given problem.  To evaluate the integration we use there WOLFRAM ALPHA.

Q: Determine the area below f(x) = 18-2x and above the line y=8+x. Sketch the graphs.

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Q: Find area of the region under the curve y=x^3−9 and above the x-axis, for 5≤x≤7. area=

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Q: the area between the curves y = x2 - 8 and y = 4

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Q: Find the area enclosed between the x-axis, the curve y= (x-15)(7-x)(x+12) and the lines x=-12 and…

A: We have to find the area enclosed between the x-axis, the curve y=(x-15)(7-x)(x+12) and the lines…

Q: Find the area of the region in the first quadrant bounded by the line y=5​x, the line x=5​, the…

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Q: Q3/ Find the area of the region in the first quadrant that is bounded above by y = with respect to…

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Q: Find the area bounded by the indicated curves. y 2x, y 4-2x, x = 0 (x20) The area is

A: Given; y=2x^2, y=4-2x , x&gt;0

Q: Find the area bounded by the curve x²=y+2 and the line x+y=0

A: Integrals and derivatives are considered as the inverses of each other. For example If we integrate…

Q: Find the area of the region bounded by the curve y = 3x -1 and the line y = 74. The area is .

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Q: Find the area bounded by the curve y = 4x - x2 and y = 3.

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Q: Find the area bounded by the curves 4y – x = 0 and y – 4x = 0 1. For points of intersection. 2. Area…

A: 4y=x2 and y2=4x1.) solving bothx242=4xx4=64xx(x3-64)=0x=0 , x3=64x=0, x=4corresponding  y-valuesat…

Q: Find the area R- region in the first quadrant that lies below the curve y=x^2+4 and is bounded by…

A: The given problem is to find the area of region R bounded below by the given curve and the line.…

Q: Solve by integration: What is the area of the region enclosed by the curve y=x(x-1)(x-2) and the…

A: See the attachment

Q: Find the area bounded by the curve y = 4x - x² and y = 3. Answer:

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Q: The area bounded by the x-axis, y = x², and y = 2 - x.

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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.