If the infinite curve  y = e−4x, x ≥ 0,  is rotated about the x-axis, find the area of the resulting surface.

Q: Find the area of the surface that is generated by revolving the portion of the curve y = x² between…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis y = v5 – x, 3 <x…

A: Given:- y=√(5-x) , [3, 5] To find:- Area of surface rotating about x axis

Q: Determine the surface area generated when a portion of the curve in the 1st quadrant of y² = 2(x² -…

A: Above question is solved.

Q: Find the area of the surface generated when the given curve is revolved about the given axis. y =…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = V5 - x, 3 <…

A: Definition used -                             Area of the surface obtained by rotating the curve…

Q: The area of the surface generated by revolving the curve y = V9 - x,-2 s xS 2 about the x-axis is…

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Q: Find the exact area of the surface generated by revolving the curve over the given interval about…

A: Given data: The given expression for the curve is y=(2x-x2)1/2. The given limits of x are [a,…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. x -(y2 + 2)3/2,…

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Q: y = V4-x, -l&xs1 about the x-axis

A: We'll answer the first question since the exact one was specified. Please submit a new question…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y=x3,…

A: If the curve y = f(x), a ≤ x ≤ b is revolved about the x-axis, then the area of the resulting…

Q: Find the area of the surface generated when the given curve is revolved about the x-axis.  y =…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = x3, 0 < x <…

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Q: Find the area of the surface generated by revolving the given curve about the X - AXIS. Y 8x, 0 < a…

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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: 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 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 about each given axis. x= 5t, y- 9t,…

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Q: Find the area of the surface generated when the given curve is revolved about the x-axis. y = V3x +5…

A: Surface area of the bounded region along x axis

Q: Find the area of the surface generated when the given curve is revolved about the y-axis. y = (x^2…

A: Solution:

Q: Find the exact area of the surface obtained by rotating the given curve about the x-axis.

A: To find the surface area of obtained by rotating the curve about x axis.   If the curve y=f(x),…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. 1 + 2x' 1 y = 1-…

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Q: y = V8 - x, 2 <x S 8

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = x³, 0 < x< 5

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Q: 35. Find the area of the surface generated by revolving the para- metric curve x =t, y = 21² (0 <…

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

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Q: Find the area of the surface generated by revolving the given curve about the x-axis. y=10x, 0≤x≤3

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Q: find the surface area of the portion of the curve x²+y²=4 from x=0 to x=2 when it is revolved about…

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Q: Find the area of the surface generated when the given curve is revolved about the given axis.…

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Q: Find the area of the surface generated by revolving the given curve about the x-axis. y = V9 -x,…

A: 3

Q: y = N|XW --- - 6x 1 <x<1

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Q: Find the area of the surface generated by revolving the curve y = /8x – x² on the interval sa <…

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Q: Find the area of the surface generated when the given curve is revolved about the x-axis. y = /5x +…

A: To find the surface area generated when y=√(5x+3) is revolved around the x-axis on [0,5]

Q: The area of the surface obtained by rotating the curve y = √√x + 1, for 0 ≤ x ≤ 2, about the x-axis,…

A: Given :

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: 6. Find the exact area of the surface obtained by rotating the curve, y = x³, 0 < x < 2, about the…

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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 exact area of the surface obtained by rotatingthe curve about the x-axis. y =√(1+ 4x)  ,  1…

A: Find the exact area of the surface obtained by rotatingthe curve about the x-axis.

Q: 35. Find the area of the surface generated by revolving the para- metric curve x = t, y = 21² (0 < 1…

A: Given: x=t y=2t20≤t≤1

Q: Find the exact area of the surface generated by revolving the curve about the incated axis over the…

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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: 35. Find the area of the surface generated by revolving the para- metric curve x =1, y= 21² (0 <…

A: Given: The curves,  x =t,  y = 2t2,   0 ≤ t ≤ 1 To find: The area of the surface generated by…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = V1 + 5x, 1<…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = V1 + 5x,…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = V8 - x, 2 s…

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Q: Find the area of the surface generated when the given curve is revolved about the given axis.…

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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 exact area of the surface generated by revolving the curve about the stated axis. y = Vx…

A: The formula for area of surface generated by the revolution of curve y=f(x) , a≤x≤b about x-axis.…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = x, 0< x< 5

A: Surface area of given curve after rotation about x axis.

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. < =v² + 2)3/2, 3…

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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.