Find the area of the surface of revolution generated by revolving about the x-axis the arc of the parabola y2=12x from x-0 to x=3.

Q: Find the surface area generated by revolving the portion of the curve y=x^2+1 between x=1 and x=2…

A: Given that, Curve, y=x2+1   We have to find the Surface Area Generated by revolving the portion of…

Q: Find the area of the surface pf revolution geneeated by revolvinh about y= -2 the arc of the…

A: Given, So, x=y212=gy ⇒g'y=y6 limit of y is from 0 to 6 The formula for finding the area is,…

Q: Find the area of the surface formed by revolving the graph of f (x) = x2 on the interval [0,√2]…

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Q: Find the area of the surface generated by revolving the curve x= cos (3t), y = 5+ sin (3t) on 0sts,…

A: Suppose parametric curve rt=xt,yt for a≤t≤b are revolving about the x-axis then surface area…

Q: 2. Find the surface area generated by revolving the circle x = cost, y = 1 + sint, 0sts2n over x -…

A: Use formula of area about x axis

Q: Find the area of the surface obtained by rotating the curve about the x-axis y=Vx, 0sxs4

A: Please refer to the image below.

Q: Find the area of the surface formed by revolving the graph of y = 2e−x on the interval [0, ∞) about…

A: Consider The infinite curve

Q: Find the exact value of the surface area generated by revolving the given curve, about the x-axis. 1…

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Q: Find the area of the surface generated by revolving the curve 1 V1 + eb", 5x 0 < x < 2 around the…

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Q: Find the surface area generated when the arc given by y = 2/15 – x; 0 <x < 15, is revolved about the…

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Q: Find the area of the surface obtained by revolving the given curve about the x-axis. on (0, In(3)

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Q: Find the surface area of revolution generated by revolving the curve y= (3x)5 over about the y…

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Q: 2. Find the area of surface that is generated by revolving the portion of the curve x = V16 – y , 0…

A: Given, x= √(16-y) Therefore, f(y)= √(16-y) Differentiating the above equation with respect to y we…

Q: Find the area of the surface obtained by revolving the graph of y = √x(4x − 3)/6, 1 ≤ x ≤ 9 about…

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Q: Find the area of the surface generated by revolving the curve y /2x-x, 0.25 sxs1.5, about the…

A: Use surface area formula about x asis

Q: Find the area of the surface generated by revolving the given curve about the x- axis: y = 19 – x²,…

A: Given,y=9-x2   squaring both the sides,y2=9-x2x2+y2=9x2+y2=32this is the equation of the circle with…

Q: Find the area of the surface generated by revolving the curve y = cos(r), 0<aS5 about the r- axis.

A: The solution is given below in the next step:

Q: Find the area of the surface obtained by rotating the parabola 1 y = 0 <x < 2, about the y-axis.

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Q: Determine the surface area generated by revolving the arc 3y= 4x from x=0 to x=3 about the x-axis.

A: To find- Determine the surface area generated by revolving the arc 3y = 4x from x=0 to x=3 about the…

Q: 5) Determine the area of the surface obtained by rotating the arc y = Vx –1 around the x- axis from…

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Q: Find the area of the surface generated by revolving the curve y = √(x2 + 2), 0 ≤x ≤ √2, about the…

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Q: The area of the surface obtained by rotating the curve y = 25-x² , -4 sx<4 about the x-axis is

A: Area of the surface rotated about x -axis is, a≤x≤b,…

Q: Find the area of the surface generated by revolving the curve about the given axis. x = 6 cos(e), y…

A: Solution

Q: Find the area of the surface obtained by rotating the parabola 1 0 <x < 2, about the y-axis.

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Q: Find the surface area obtained by revolving the parabolic arc y2=x from (0, 0) to (9, 3) about the…

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Q: Solve the area of the surface of the revolution generated by revolving the arc of the curve, x= y³…

A: A detailed solution is given below.

Q: Find the area of the surface generated by revolving the curve - 5x y = e-b", x > 0 around the -axis.

A:

Q: Find the area of the surface generated by revolving the curve y=−x^3/18​, −2√2≤x≤0​, about the​…

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Q: Find the area of the surface generated by revolving the curve - 5x y = e x > 0

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Q: (d) Find the area of the surface generated by revolving the curve y = 2a, 0 < x < 3, about the…

A: Part (D) To find the area of the surface generated by revolving the curve, y=2x,0≤x≤3, about the…

Q: Find the surface area of the solid gained by revolving the curve 0 < x < 14, about the x – axis. 14'

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Q: Find the area of the surface generated by revolving the curve y = - V6 sxs0, about the x-axis. 24'

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Q: Find the area of the surface generated by revolving the given curve about the x-axis. y=6x, 0≤x≤3

A: Find the surface area generated by revolving the given curve about the x-axis.

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y= square root…

A: The given curve is

Q: 7 Find the area of the surface generated by revolving x = 2/4-y, 0sys about the y-axis.

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Q: Find the area of the surface obtained by rotating the curve y=1+3x² from x = 0 to x = 9 about the…

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Q: Find the area of the surface formed by revolving the graph of y = Vx + 2 on the interval [1,8] about…

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Q: Find the area of the surface generated by revolving the curve y=- 24 .Osxs/6. about the x-axis.

A: area = ∫06 ydx area = ∫06  x3dx/24 area = [x4/96]60 area = 6*6/96 - 0 area = 3/8

Q: . Find the area of the surface generated by revolving the given curve about the -axis. x = 9y + 1,0…

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Q: Find the area of the surface generated by revolving the curve y = sqrt 2x-x^2, 0.25 less than or…

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Q: Find the area of the surface generated by revolving the curve y = 2√x, 1≤x≤2, about the x-axis.

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Q: Find the area of the surface that is generated by revolving the portion of y=x2 between x=1 and x=2…

A: To the area of the surface that is generated by revolving the portion of y=x2 between x=1 and x=2…

Q: Find the surface area of revolution about the x-axis of y = 5 sin(4x) c

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Q: Y = e-5x x > 0

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Q: Find the area of the surface generated by revolving the curve 1 V1+e*, 5x 0 < x < 2 around the…

A: We can find the area of the the surface as follows

Q: Find the area of the surface generated by revolving the curve y = 3/x, 1 < x <4 about the x axis.

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Q: Find the area of the surface generated by revolving the curve about each given axis. x = 6t, y = 9t,…

A: Here,  we need to find the surface generated by revolving the curve x=6t, y=9t, 0≤t≤3, about each…

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.