Find the surface area of revolution about the x-axis of  y= 4sin(4x), from x is greater than or equal to 0 and less than or equal to pi/2

Q: Find the surface area of revolution about the y-axis of y = 3 – 3x over the interval 0 < x <1

A: Given

Q: Find the surface area of revolution about the x-axis of y = 3x + 4 over the interval 1 < x < 2

A: Answer

Q: Find the area between the curves y = 4 cos(6x),    y = 4 sin(12x),    x = 0,    x = π/12

A: Given,

Q: Compute the surface area of revolution about the x-axis over the interval [0, n] for y = 8 sin(x).…

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Q: Find the surface area of revolution about the x-axis of R.

A: Given curve y=2x, 2.3≤x≤4.2 We have to find the surface area of revolution.

Q: Compute the surface area of revolution about the x-axis over the interval [0, 1] for y = 4x³.

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Q: Find the surface area of revolution about the y-axis of y= x^2/9  over the interval 0≤x≤6. Enter…

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Q: Compute the surface area of revolution of y=sinxy=sin⁡x about the x-axis over the interval [0,7π]

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Q: Find the surface area of revolution about the x-axis of y = 7x +7 over the interval 2 <x < 3

A: Given function,     y=f(x)=7x+7, 2≤x≤3f'(x)=dydx=7Here lower limit is 2 and upper limit is 3

Q: If the curve y = ln x between x = 1 and x = e is rotated about the y-axis, which integral below…

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Q: 7) (g) Set up and evaluate the definite integral for the area of the surface generated by revolving…

A: we use integration formula for area of surface rotating about x-axis..

Q: Compute the surface area of revolution about the x-axis over the interval [3,6] for y = 4x + 4. (Use…

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Q: Find the surface area of revolution about the x-axis of y=5x+7 over the interval 0≤x≤3

A: S=∫2πydsds=1+dydx2

Q: Compute the surface area of revolution about the x-axis over the interval [0, 1] for y = e (Use…

A: Solution is given below

Q: Find the surface area of revolution about the x-axis of y 4x +7 over the interval 0 < r<3

A:

Q: Find the area under one arch of the cycloid x = a(t-sint) , y = a(1-cost)

A: Introduction: A cycloid is a two-dimensional curve that is constructed with half circles. One arc of…

Q: Compute the surface area of revolution about the x-axis over the interval [0, n] for y = 6 sin(x).

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Q: 2.) Set up and evaluate the definite integral for the area of the surface generated by revolving the…

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Q: Set up and evaluate the definite integral for the area of the surface generated by revolving the…

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Q: Set up the integral for the surface area of the solid created by revolving y= Vx 1< x <8 about the…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find the surface area of revolution about the x-axis of y = 7 sin(3x) over the interval 0 < x <

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Q: Compute the surface area of revolution about the x-axis over the interval [3, 5] for y = 2x + 4.

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Q: Find the surface area generated by revolving about the y-axis that part of the curve y = In x lying…

A: Solution We have to find the Surface area generated by revolving about the y-axis the part of curve…

Q: The base of a lamp is constructed by revolving a quarter circle  y = (2x-x^2)^0.5  around the…

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Q: Find the surface area generated by revolving Y=(x^3)/6 about the x axis over the interval [0, sqrt6]

A: qqq

Q: Sketch the region bounded above by the curve (9e^−x)*sin(πx), the x-axis, and x = 1, and find the…

A: We have to sketch the region bounded by the curve 9e-xsinπx, x-axis, and x=1, and also find the area…

Q: Compute the surface area of revolution about the x-axis over the interval [0, 1] for y = 4x³. (Use…

A: In this question we have to find the surface area of the revolution about the x-axis.

Q: Find the surface area of the solid that results when the region in the first quadrant bounded by the…

A: The curve is x2+y2=82

Q: 3. Find the surface area generated by rotating y=- bounded by y=0_ x=0 , and x=9 about the the…

A: Surface area generated by rotating a curve y = f(x) about the x-axis from x = a to x = b is given by…

Q: Find the surface area of revolution about the x-axis of 5z +3 over the interval 1 < z < 2

A: y=5x+3 &amp; given interval 1≤x≤2As we know surface area of revolution abput x-axis from x=a to…

Q: compute the surface area of revolution about the x-axis over the interval

A: The given function is

Q: Find the surface area of revolution about the x-axis of y=7x+1 over the interval 1 ≤ x ≤ 3

A: The given equation is y=7x+1 over the interval 1≤x≤3. Calculate the surface area of revolution about…

Q: Set up and evaluate the definite integral for the area of the surface generated by revolving the…

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Q: Evaluate the definite integral that represents the area of the surface generated by revolving the…

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Q: Compute the surface area of revolution of y=sinx about the x-axis over the interval [0,π].

A: Given data: The expression for the given function is y=sinx. The given interval of x is [a,b]=[0,…

Q: Find the surface area of revolution about the x-axis of y=7sin(5x) over the interval 0≤x≤π/5

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Q: the x-axis of y=2sin(4x) over the interval 0≤x≤π4

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Q: Find the surface area of revolution about the x-axis of y = 2 sin(4x) over the interval 0 <I<

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Q: Compute the surface area of revolution about the x-axis over the interval [0, r] for y = 3 sin(x).…

A: We need to find surface area.

Q: Find the integral that represents the surface area obtained by rotating around the x-axis the graph…

A: To find the integral representation for the surface area under the given conditions.

Q: Find the surface area of revolution about the x-axis of y 7x + 7 over the interval 0 < a < 3

A:

Q: Compute the surface area of revolution about the x-axis over the interval [0, x] for y = 5 sin(x).…

A: Recall: Area of the surface of revolution about x-axis:    If the curve y=f(x) , a≤x≤b is rotated…

Q: Compute the surface area of revolution of f (x) (x + 1)z about the x-axis over 3 [0,1]

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Q: Find the surface area of revolution about the x-axis of 3 sin(7x) over the interval 0 < z <

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Q: Set up and evaluate the definite integral for the area of the surface generated by revolving the…

A: y=16-x2,  -1≤x≤1 Differentiating with respect to x, we get…

Q: Find the surface area of revolution about the x-axis of y= 3sin(5x) over the interval 0 ≤ x ≤ π/5

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Q: 6. Write and evaluate the definite integral that represents the area of the surface generated by…

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Q: Find the surface area of the solid that results when the region in the first quadrant bounded by the…

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Q: Compute the surface area of revolution about the x-axis over the interval [0, x] for y = 8 sin(x).…

A: solution:-y=8sinxx∈[0, π]revolution about the x-axissurface area of…

Q: Find the area of the surface obtained by rotating the curve y = ln(1 — x2), 0 ≤ x ≤ 1/2 about the…

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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.