Determine the area of the surface of revolution of x=sqrt{y} from (1,1) to (2,4), rotated about the y-axis.

Q: Find the area of the surface generated by revolving the curve = V¤ + 3, 4 < y <7

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Q: 13. Find the area of the surface generated when the curve y = -, on [2,4] is rotated about the…

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Q: Find the surface area of the cone frustum generated by revolving the line segment y = (x/2) + (1/2),…

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Q: Find the surface area of the portion of the sphere generated by revolving the curve y = 1- x, 0 <xs;…

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Q: 10. у %3D /5 — х, 3 <x < 5

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Q: 2) Find the exact area of the surface obtained by rotating the curve about the x-axis. y = /1 + 4x,…

A: We can use the application of integration in order to solve the given problem.

Q: Find the area of the surface generated by revolving the curve y = Vx + 3, 4 < y <7 around the…

A: We have to find area of the surface . Given y=x3+3                                 4≤y≤7

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

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Q: Find the area of the surface generated by revolving the curve about the y-axis. y=4-x², 0≤x≤2.

A: In this question we have to find the area of the surface generated by revolving the curve about the…

Q: Find the area of the surface generated by revolving the curve x = Vy, 0<y <4, about the y-axis.

A: We will use standard method.

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

A: find dy/dx and solve for ds.

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

A: Given: The equation of the curve y=x36+12x,where  12≤x≤1. Calculation: Compute the surface area as…

Q: Find the Area of the Surface obtained by rotating the curve about the y -axis y = √√x, 1 ≤ y ≤2

A: Given y=x13    1≤y≤2Rotating about y-axisarea of surface of revolution about tghe y…

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 exact area of the surface obtained by rotating the curve about the x-axis. X = 2 + 3y2, 1 <…

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Q: Find a unit normal to the surface x'y + 2xz = 4 at the point (2,-2,3).

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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: 2. The surface area of the surface generated by revolving the curve y = x, -1 < x<1, about the…

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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 portion of the cylindrical surface y = 4 - x2 in the first octant that is…

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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: Find the exact area of the surface obtained by rotating the curve x = (1/3)y^3, 0 &lt;= y &lt;= 1,…

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Q: y = } + sxs1 <x<1 2

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Q: 5- Find the area of the surface generated by revolving the curve X= (y*/4) +1/ (8y²),1<y <2 ,about…

A: Given:function: x=y44+18y2Interval: 1≤y≤2To find : Area of surface generated by revolving the curve…

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

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Q: Find the equation of the surface of revolution of x = z2 about the x-axis.

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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: Find the area of the surface obtained by rotating the curve y = x about y-axis for 1< y< 3.

A: We have to find surface area

Q: Find the area of the surface obtained by rotating the curve y = x², 0 < x< 1, about the y axis.

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Q: Find the area of the surface obtained by rotating the curve x = 3 (y + 2)3/2, 1 <y< 2, about the…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. x = 1/3(y2 +…

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Q: Find the curved surface area of the solid generated by revolving the part of the curve y=x² from…

A: Given curve is                                               y=x2 from     (0, 0) to (6, 6) Rotation…

Q: . Find the area of the surface generated when the curve y = x* 1 + ,on [1,2] is rotated about the…

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Q: Find the area of the surface when y = vx, from (4, 2) to (9, 3) is rotated about the x-axis.

A: Surface area formula for rotating about x-axis is S=∫2πydS where dS=1+dydx2dx

Q: Find the area of the surface obtained by rotating the curve y = 2x 223 from x = 0 to x 2 about the…

A: HERE THE LIMITS OF INTEGRATION IS 0 to 2.

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

A:

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: Find the exact area of the surface obtained by rotating the curve about the x-axis. x = 5 + 4y2,…

A: We use the formula S=2π integration of y √(1+x'2)dy from 1 to 2

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

A:

Q: Find the area of the surface of revolution generated by revolving C = {(x,y):x = y = 1- 2t, -1sts1}…

A: Given that C=x,y:x=-3+4t3, y=1-2t, -1≤t≤1 about the line x=2. The range of y is,…

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 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 area of the surface obtained by rotating the curve y=1/3 x3/2, 0≤y≤12  about the y- axis.

A: Let a rectangular strip parallel to x-axis of thickness dy be made whose tip touches the curve…

Q: Give an equation of the surface of revolution generated by revolving x In z about the z-axis.

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis.  x=1/3(y2 + 2)…

A: The given curve is,

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: ii) Find the exact area of the surface obtained by rotating the curve 1 12x 3 y = x³ + 9 1 ≤ x ≤ 2,

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

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Q: Calculate the area of the surface of revolution obtained by revolving the curve x = 1/3 (y2 + 2)3/2…

A: To find the area of the surface of revolution

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.