10.Which of the expressions below could be used to correctly compute the area bounded by the graph y = 10x – 4x² and the line y = 2x. (A) L, 8x – 4x² dx - (B) S 4x² – 8x dx (C) S,8– 8x dx (D) S 8x – 4x? dx (E) S 4x² – 8x dx

Q: What is the area (in square units) of the region bounded by the graphs of y=x2+2, and the x axis…

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Q: Find the area bounded by the parabola y^2=4x and the line 2x-4. (with graph)

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Q: 18.Find the area bounded by the graph y = 30x – 3x² and the x – axis. %3D

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Q: What is the area (in square units) of the region bounded by the graphs of y=x+2, and the x axis from…

A: topic - area under the curve

Q: 4.) Find the area of the region bounded by the curves y =x- 6x? + 8x and y =x - 2x

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Q: 5. Find the area bounded by the curves y = x4 – 4x2 + 4 and y = x2. -2

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Q: Compute the area bounded by the curve y = 3x - x2, the x-axis and the ordinates x = 2; x = 4.

A: We need to evaluate the area bounded by the following curve : C1 : y = 3x-x2 C2 : x -axis C3  : x =…

Q: Find the area bounded by the curve x^2 + 4y - 8 = 0, the x - axis, and the lines x = 3 and = 5

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Q: What is the area (in square units) of the region bounded by the graphs of y=r²+2, and the x axis…

A:

Q: 10.Which of the expressions below could be used to correctly compute the area bounded by the graph y…

A: The given function is y=10x-4x2   and  y=2x

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 bounded by the following curves and lines  y = 3x/square root of x+4  where y = 0 and…

A: The given region are: y=3xx+4, y=0, x=4

Q: 2. Find the area of the region bounded by the curve y = x^3 − 2x^2 − 5 x + 6, the x-axis, and the…

A: Given: y=x3-2x2-5x+6 For finding area of region bounded by given curve with x-axis and the lines…

Q: 29. Find the area of the region bounded by y =. = x2 + 3x + 1 and y = 6x - 1. [4.4]|

A: If two curves f(x) and g(x) defined over the interval [a,b], then the area bounded by the curves…

Q: 1/ Find the area of the region enclosed between the curves y= 2x²+10 and y=4x+16 and ,x=-2 and x-5?…

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

Q: у 3 4/x, у-4y + 2х %3D 5 2x = 5

A:

Q: 7. Find the area of the region bounded by the graph of y= 2x² – 3x+2, the x-axis, and the vertical…

A: The equation of the curves are: C1: y = 2x2-3x+2C2: y = 0C3: x = 0C4: x = 2 To evaluate: The area…

Q: 2. Find the area bounded by the two curves y = x² - 6x²+ 8x and y = x² - 4x.

A: We have to compute the area between the given curves using the double integration method by first…

Q: 3. Find the area of the region bounded by y=x²-2x +2 and y=6-x².

A: Use area under curve

Q: 1/ Find the area of the region enclosed between the curves y= 2x+10 and y=4x+16 and ,x=-2 and x-5?…

A:

Q: 7. Find the area bounded by the curve y = 4x - x^2 and the lines x = 0 and y = 4.

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Q: I. FIND THE AREA BOUNDED BY THE FF CURVES AND LINES: 1. The loop of y = x *(4 - x) 2. у %3 бх - х, y…

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

Q: .2 What is the area (in square units) of the region bounded by the graphs of y=x+2, and the x axis…

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Q: 4 Find the area of the region bounded by x = 2y²+1 and the y-axis using the horizontal strip.

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Q: 3) Find the area bounded by the curves: x² – 4x + 1 = 3y and x2 + 2x + 2y – 5 = 0.

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Q: 1/ Find the area of the region enclosed between the curves y= 2x2+10 and y=4x+16 and ,x=-2 and x=5?…

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: 31. Find the area bounded by the parabola y-3x +3 = 0 and the line x 4. %3D y-axis X-axis 1

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Q: 7) Determine the area bounded by the x-axis under the line y = 2x+1 from x=1 to x=4

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Q: What is the area of the region between y=x²-2x-3 and the x-axis from to 6? x=0

A: Area bounded by the curve fx=x2-2x-3 and x-axis on interval 0, 6

Q: What is the area under the graph of y = 2 54-3-2-1 O O N/W 13 2 15 2 ਜਾਨ , -2+ -3 4 1 2 3 4 5 X on…

A: The region is bounded by the graph y=2-x on the interval -2,1

Q: 3. a. Find the area of the region bounded by y= 2x2 + 10, y = 4x + 16, x = -4 and x = 5.

A: As per bartleby guidelines we only give first question answer.

Q: What is the area bound between the curve y= \x/2 and the x-axis between x =-3 and 4/2 - 2/3 3 x = 2?…

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Q: 8. Find the area between the curves y = x x² and y = x2 – 4x between x = O and x = 2.

A: For calculating the area between curves first of all we will draw the schematic diagram of the…

Q: 2. Find the area between between x = 0 and x =9. y=√x-10 and y=0 10

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Q: Find the area of the given region. 5 y = 16 + x2 y 0.5 0.4 0.2 0.1 -1 1 4 -0.1 4 2.

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Q: 2. Find the area of the region bounded by y = 2x² +10, y = 4x+16, x = -2, and x = 5.

A: first draw bounded region then find limit of region and using vertical strips find the area

Q: Find the area between the curves: y=x^3-11x^2+18x and y = -x^3+11x^2-18x

A: y=x3-11x2+18x and y=-x3+11x2-18xTo find the area between the curves:

Q: Find the area of the region bounded by y = -4x + 9, y = 2x? – 11x + 9, and the lines x = -2 and x =…

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Q: 10.Which of the expressions below could be used to correctly compute the area bounded by the graph y…

A: Given Data: Equation 1: y=10x-4x2 Equation 2: y=2x The intersection points of two curves. Substitute…

Q: 6. Find the area of the region bounded by the two curves of equat rens a) x=3-y² and f(x)= 3x (スー2)-…

A: Note:- In Part (a), you mention f(x) for 2nd curve but it is not mentioned for first curve. If i…

Q: 3. Find the area bounded by the curve y = x² - 7x + 6 and the x-axis and the ordinates x 2 and x =…

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Q: y = 2x ,2 y+ 4x – 8 = 0

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Q: 3. Find the area bounded by the curve y 4sin(2x), the x-axis, and the lines x = 0 and x =

A: We have to find the area bounded by the given curves. We will find the area by the help of…

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A:

Q: FIND THE AREA BOUNDED BY THE FF CURVES AND LINES: The loop of y^2 = x^4 (4-x)

A: We have to find the area bounded by the loop  y2 = x4(4 - x)

Q: 2. Find the area of the region enclosed by the parabola y = 2 – x² and the line y = -x.

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Q: 3 2. Find the area bounded by the two curves y = x³- 6x² + 8x and y = x² - 4x.

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Q: What is the area of the region between  y=x^2 -2x-3 and the x-axis from x=0 to 6?

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Q: Compute the area bounded by the curve y = x2 + 3, the x-axis and the ordinates x = 1; = 4.

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Q: 1/ Find the area of the region enclosed between the curves y= 2x+10 and y=4x+16 and,x=-2 and x-5?…

A: We use integral to find area bounded by curve and lines

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.