Calculate the total area of the region described. Do not count area beneath the x-axis as negative. HINT [See Example 6.] Bounded by the curve  y = 4 − x2,  the x-axis, and the lines  x = −2 and x = 4

Q: 3. Find the area of the region enclosed by the curves y = x² + 2, y = -x, x = 0, and x = 1. (a) (c)…

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Q: Q4. : Find the area of the region R enclosed by the curve y=x+2. Y3DX2 and the line

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

A: Area under the curve is given by integration over required interval

Q: Calculate the area of the region bounded by the curves x = y? and x = (2 – y²)². Explain your…

A: We will first solve where the equations meet for y. y2=(2-y2)2…

Q: Find the area of the region bounded by the curves y=x4 andy=2x-x²

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Q: (10,00 Puanlar) 6- Find the area of the region bounded by the curves y – 3x = 4 and 3x- 2y = 11. 124…

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Q: 2) Find the area bounded by the curve y=x² + x + 4, the x-axis and the lines x = 1 and x = 3. (Draw…

A: Given information: The curve given is y=x2+x+4, x-axis and the lines x=1 and x=3. The area of our…

Q: Find the total area of the region between the curve and the x-axis. 24) y = x2(x- 2)2; 0sxs2 15 A) -…

A: The graph of the bounded region is as shown above. As shown draw a stipe parallel to y-axis. So, y…

Q: Let b 1 be an integer. The area of the region bounded by the graphs of the functions y = 20bx and y…

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Q: Find the area of the region(s) enclosed by the curve y = |2x - 6|, the x-axis, and the lines x = 0…

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Q: Sketch the curve and find the total area between the curve and the Given interval on the x axis…

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Q: Find the area between the y-axis and the graph X = Y 7 6 5 4 X 543-2/1² 1 2 3 4 5 WŃ y - 1 on the…

A: Here we have to use the concept of integration

Q: 7. Find the area enclosed by the x-axis and the curve y = -x² + 9. 32 s.u. а. b. 18 s.u. с. 36 s.u.…

A: Area enclosed by the curve y=-x2+9.

Q: Q3: A common region defined by two functions: x= 2, and x? + y? = 4. The form of the double integral…

A: Function x2 + y2 = 4 is a circle whose center is at origin and has radius of 2.

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: The area of the region bounded by the curve y=e, the x-axis, the y-axis, and the line x 2 is equal…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Calculate the area of the region bounded by the curves ? = ?² and ? = (2 − ?²)². Explain youranswer

A: Given curves are    x=2-y22 and x=y2   !st we need to find the points of intersection of the two…

Q: 1. the loop of y? = x * (3 - x) %D

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Q: Find the area of the region between the graphs of y = 16-2² and y = -4≤ ≤ -1. The area is 2x+8 over…

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Q: (10,00 Puanlar) 6- Find the area of the region bounded by the curves y - 3x = 4 and 3x- 2y = 11. 134…

A: The given curves are: y2-3x=43x-2y=11

Q: 17-Graph of the function y = x^3 What is the area of the region bounded by the lines y = 0, y =1 and…

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Q: Q4) Find the area of the region bounded by the lines ( y=x ), (y=2-x) &(x=1).

A: To find the area of the region

Q: Q2) Find the area of the region bounded by the (y=v-x ), (y2=x+2) & ( y3=0).

A: Take strip along x axis and solve it.

Q: Graph the equations and shade the area of the region between the curves. y - e, y-e4x - 3 and x- o…

A: first, we will draw the graph of the function y=ex and y=e4x-3 and then evaluate the area under the…

Q: 7. Find the area of the region bounded above by the line y 3, below by the graph of y VT, between…

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

A: From the given curves the bounded region is as shown below:

Q: 3. Find the total area between the given region and the x-axis .2 a) y = -x - 2x,-3 < x < 2 b) y =…

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Q: 1 2. Find the total area of the region between the curve and the x-axis. a. y=2-x; b. y= 3x-3;…

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Q: b) Find the total area between the region and the x- axis. y= x – 4x ; -2<x<2

A: Given equation is                    y=x4-4x

Q: Find the area of the region bounded above by y = x + 6, bounded below by y = x2, and bounded on the…

A: Area of the region

Q: 2 Sketch the graph of y = 0.5x +2. Find the area between your line, the x-axis and the lines x = 0…

A: The slope-intercept form of a line is given by the equation y=mx+c. Here, m represents the slope…

Q: 6. Find the number a such that the line x = a bisects the area under the curve y = 1 1< x < 4.

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Q: a) Find the area of the region enclosed by the curves y = 12 – x² and y = x? - 6. Answer: A =

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: (c). Find the area of the region enclosed by the graphs of y=\x+3,x=-3 and y=2.

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Q: (c) Calculate the area of a region bounded by the curves y = -x and y = -x, the line y = -3, and y =…

A: Given the curve y2=-x and y=-x2, the line y=-3 and y=2

Q: Evaluate (x - y)dA where R is the region above the x -axis bounded by y = 3x R. and y? = 4 - x.

A: First we integrated with respect to X-axis and then with respect to Y-axis.

Q: 7. What is the area bounded by the curve y=x and the line x-4=0? A. 10 32 B. 3 C. 32 D. 11

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Q: Sketch the region bounded by the curve 3xe¯", the x-axis, and x = 4, and find the area of the…

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Q: 5. I Find the area of the region enclosed by the curves y = 3x³ - x²-10x and y=2x-x². (x ≥ 0) (a)…

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Q: What is the area of the region bounded above by y = -x- + 8 and below by y = x? 54 $2 14 1 23 4 5 64…

A: This is a problem related to integration. Based on the formula of area bounded by given region we…

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

A: Here we find the area using integration.

Q: Find the area between the y-axis and the graph X = -y + 5y – 4 on the interval [1, 4]. 3- 2- 54 3-2…

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Q: 4.5x follows. A sketch of the region enclosed by y = x and y = a2 + 1 2- -2 -1 -2 Area of the region…

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

Q: Find the area of the region bounded by y²-x=0 and y²+x=2₁ (A) u² 3 В) (√2-1) u² 3 C 8u² D s-u² B

A: Area bounded by two curves: y2-x=0 and y2+x=2

Q: Let R be the region bounded by the x-axis and the graphs of and y = 4 – 2.x , as shown in the figure…

A: Since you have posted multiple questions but according to guidelines we will solve the first…

Q: Solve for what is asked. 1. Find the area of the region bounded by f(x) = x³, the x-axis, and the…

A: This question is based on application of Integration.

Q: Q8 Find the area of the region enclosed by the curves: y = x³, y = x, x > 0.

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Q: 2. Find the total area of the region between the curve and the x-axis. a. y=2-x; 0≤x≤3 b. y=3x²-3;…

A: Topic:- application of integration     Note :- as per our guideline if more than three subparts…

Q: Find the area of the shaded region. y 3- x = y - 2 y = 1 x= e X -3 -1 (1 2 3 4 y = -1 -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.