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

Q: Find the surface area of the object obtained by rotating y = 1 +. 8x2 , 2<x 3 about the x-axis. 4

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Q: Find the area and centroid bounded by the curve 5y? = 16x and the curve y2 = 8x – 24.

A: Since you have asked multiple question, we will solve the one question for you. If you want any…

Q: The area of the surface obtained by rotating the curve y = 22 x + 1, 0 < x < 44 about the x-axis is

A: Consider the given curve. y=22x+1 in the interval 0≤x≤44 The problem requires to find the area of…

Q: Find a parametrization for the cylinder x^2 + y^2 = 4.

A: Given: x2+y2=4

Q: Find the equation of the plane tangent to the surface G(x,y, z) = 2x² - y² – 3z2 = -4 at P = (-2,…

A: Given surface is                                                G(x, y, z): 2x2-y2-3z2=-4 we have to…

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: * = Vy +5,

A: We have to evaluate the area of the surface generated by revolving the curve  x=y+5 between the…

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 equation of the tangent plane to the surface z=9x^5+2y^5+1xy at the point (0,−1,−2) z=

A: From tangent plane equation to a curve

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: Integrate ƒ(x, y) = sqrt(4 - x2) over the smaller sector cut from the disk x2 + y2 &lt;=4 by the…

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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: The area of the surface obtained by rotating the curve y = x2, 0 <x< 12 about the y-axis is

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Q: Find the points on the surface ( y + z)^2 + (z - x)^2 = 16 where the normal line is parallel to the…

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Q: Find the center of mass and the moment of inertia about the y-axis of a thin plate bounded by the…

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Q: Find the area of the surface obtained by rotating the curve }=2,3 from z = 0 to z = 1 about the…

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Q: Find the area of the surface obtained by rotating the curve y = 4x + 4, 0 < x< 8, about %3D the…

A: To find- Find the area of the surface obtained by rotating the curve y2 = 4x + 4, 0 ≤ x ≤ 8, about…

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 one side of the “wall” standing orthogonally on the curve 2x + 3y = 6, 0&lt;=x&lt;=…

A: To Determine: Find the area of one side of the “wall” standing orthogonally on the curve…

Q: Find the area of the surface. The part of the plane x + 2y + 3z = 1 that lies inside the cylinder x²…

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Q: Find the points on the surface 2a2 + ly² + 522 = 1 at which the tangent plane is parallel to the…

A: We will use the following method for finding the two required point.

Q: Find the surface area for the object obtained by rotating y=7x+2 about the x-axis over the interval…

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

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Q: Find the points on the surface 6x² + y² – 3z² = 4 where the tangent plane to the surface is parallel…

A: We need to find points of intersection.

Q: Find the surface area of the portion of the surface x2- 2 In a+ V15 y - z = 0 above the rectangle 1…

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Q: . Find the area of the surface obtained by rotating y = S, Vs² – 1 ds, 1 < x < 2 about the y-axis.

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Q: The area of the surface obtained by rotating the curve y = V25–x2, -4 < x s 4 about the x-axis is

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Q: Find the exact area of the surface obtained by rotatingthe curve about the x-axis. 9x =y2 + 18 ,  2…

A: Consider the curves, 9x=y2+18,  2≤x≤6 Differentiate the given curve with respect to “y” then,…

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

A: To find the surface area of the object obtained by rotating y=x36+12x ,  1≤x≤2 about x-axis.  Let,…

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 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 a point on the surface z = 3x^2 − y^2 at which the tangent plane to this surface is parallel to…

A: We need to find the Point on the surface of  z=3x2−y2 given tangent plane to this surface is…

Q: Find the length of the curve y =Vx³, for [0, 4]. Find also the surface area of the region is rotated…

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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: 4. Find the area of the surface generated by revolving the curve y = v9 – x², - 2 < x < 2, about the…

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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 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 area of the surface generated when y² = 12x is revolved about the x- axis from x = 0 to x =…

A: Given curve,y2 = 12xRevolved about x-axis from x=0 to x=3.

Q: The area of the surface obtained by rotating the curve y = V4-x², -2 s xs 2 about the x-axis is

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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 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 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 =÷x/2 – x³/2 for 0 < x < around the…

A: We find dy/dx using power rule

Q: Find the surface area of the object obtained by rotating x = Vy-6 2sys3 about the y-axis.

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Q: Find the area of the surface resulting from rotating the curve: x=5t−1, y=2t^3, -2≤t≤1, around the…

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Q: Find the surface of revolution of the curve y = 4 + 3x² that is rotated about the y- axis between 1…

A: We have to find the area of the surface of revolution of the curve y=4+3x2 that is rotated about the…

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: 2. Find the area of the surface obtained by rotating the curve: y = Vx +1,1<x<5 about the Х-ахis

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Q: Find the area of the surface obtained by rotating the curve y² = 4x + 4 0<x<8 about the x-axis?

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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.