Find the surface area of the solid obtained by y=2x, 0sx58revolving around the x-axis

Q: Find the volume of the solid formed by revolving the area bounded by the parabola y2 = 9x and the…

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

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Q: Determine the surface area of the solid obtained by rotating y=v9-x from -2sxs2 about the x -axis.

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Q: Find the volume of the solid generated by revolving the curve y? – x8 – x2 = 60 between x = 0 - and…

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Q: Calculate the area of the surface generated when the curve, y = Vx is revolved on the interval [1<…

A: Consider the equation

Q: nd the volume of the solid generated by revolving the area bounded by y = x2 a axis from [0, 2]…

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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 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: Find the volume of the solid formed when the area of the region bounded by the curves x2- 3y=8 and…

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Q: Find the surface area for the solid of revolutic -1< x<1 about the x-axis.

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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: Find the surface area generated by revolving x=sqrt(8y-y^2) about the y axis on the interval: y=…

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Q: Q5/ Find the area of the surface generated by revolving y = where 0 <x <2, about the X-axis.

A: Given that the area of the surface generated by revolving y=x39 where 0≤x≤2 about x-axis.

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

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Q: Compute the surface area of the solid obtained by revolving the region between the x-axis and the…

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Q: Find the volume of the solid generated when the region between y = sinx and y = 0 for 0 ≤ x ≤ π is…

A: y=sinx  &amp;  y=0  for  0≤x≤π

Q: Find the area of the surface obtained by rotating the region y = x°, 0<x < 3 about the x-axis.

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Q: Find the surface area of revolution about the x-axis of y = 2x + 7 over the interval 0 <x <1

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Q: Find the surface area of revolution about the y-axis of x 36 – y? over the interval 0 < y < 2 -

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Q: Find the surface area give y^2 +4x =2lny, 0, 0≤y≤3  ; about the  x-axis.

A: We have to find the surface area give y2 + 4x = 2lny , 0 ≤ y ≤ 3 ,  about the  x-axis.

Q: Find the surface area generated by revolving y=7x+6 about the x axis on the interval [0,6]

A: We need to find the surface area generated by revolving y=7x+6 about the x axis on the interval…

Q: 4. Determine the surface area of the solid obtained by rotating y = v9 – x², -2 <x<2 about the x –…

A: Let's find.

Q: Find the area of the surface oblalned by rotating tne curve y = V4x x = 0 to x = 3 about the x-axis.…

A: Below is the solution:-

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

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Q: 2. Find the surface area when y = 2\x with 1 < x < 3 is rotated around the x axis.

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Q: Q10 Find the area of the surface generated by revolving the region bounded by, x6 1 y =6+ 16x4 1<x<3…

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Q: 4. Determine the surface area of the solid obtained by rotating y = v9 – x2, -2 < x<2 about the x -…

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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: Find the surface area generated by revolving y=5x+2 about the x axis on the interval [0,6]

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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: f(x) = x², with 0< y < 4

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Q: The volume of the solid generated by revolving the curve y = 2 x, between x =0 and x=3 about the x-…

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Q: Find the surface area of revolution about the x-axis of y = 3x + 2 over the interval 0 < z <1

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Q: 2. Find the area of the surface obtained by revolving the curve g(x) = Vx +1 on the interval 0 < x <…

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

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Q: 12. Find the surface area of the solid obtained by rotating about the x-axis for 1sxs3.

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Q: find the surface area by rotating the curve about the y-axis; y=x^3 from x=0 to x=2

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Q: Find the volume of the solid of a revolution bounded by the graphs of f(x) = – x² + 5x – 4 and y = 0…

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Q: Find the surface area of revolution about the x-axis of y 6x + 3 over the interval 2 < x < 5

A: In the question the curve given is - y=f(x)=6x+3 , 2≤x≤5 We need to find Surface area of revolution…

Q: Find the surface area of revolution about the y-axis of y = 12 – 3x? over the interval 0 < x < 2.

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Q: D Find the area of the surface generated by revolving the region bounded by, 1 1 <x < 5 4 8x2 about…

A: In the question we have to find area of the given function.

Q: Find the volume of the solid formed when the area of the region bounded by the curves x²- 3y-5 and…

A: Solution

Q: Find the surface area obtained by rotating y = V9 – x2 ,-2sxs-1 9– x² -2sxs-1

A: Given,             y=9-x2 , -2≤x≤-1

Q: Find the surface area obtained by rotating y = V9 – x² -2sxs-1

A: As we know that; The expression for the area of surface rotating about the x-axis. S=2π∫abfxf'x2+1dx…

Q: Find the surface area of the curve f (x) = x over [1,2| rotated .3 3 about the – axis -

A: The revolution of the curve y = f(x) around the x-axis is: S=2π∫abf(x)(f'(x))2+1dx

Q: Find the surface area of revolution about the x-axis of y = 6 sin(7x) over the interval 0 < x < 7

A: Here we have y=6sin(7x)  We have to find surface area of revolution about x axis in interval 0 to…

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

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Q: Find the surface area generated by rotating y=(1/3)x^3 bounded by y=0 , x=0 , and x=9 about the 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.