The given curve is rotated about the y-axis. Find the area of the resulting surface.

Q: 6. Consider the circle (x - 2)2 + y² = 1. Sketch the surface obtained by rotating this circle about…

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Q: Problem The Circle xiy² a? is rotated about the x- ascis, find the Jolume of the Solid geverated 2.

A: Find the attachment

Q: the circle is the tangent to both x and y axis. A point on the circle is (2,1). Calculate the area…

A: This question is based on Circle.

Q: In  the given equation as  follows , find the area of the surface generated by revolving the curve…

A: Given: x=t ; y=4-2t; 0≤t≤2To find the area of the surface generated by revolving the curve about…

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

A: y= 21+ sqrt(441−x2) between the points ​(21​,21​) and sqrt(1763)/2,43/2​; about the​ y-axis

Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = 1/3x3/2,…

A: The formula to find surface area is ∫2πx1+dydx2dxgiven interval is from 5 to 21 take derivative with…

Q: Calculate the surface area of the following: the portion of the parabola y x², from x = 0 to x = 2…

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Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = Vx, 1sy& 4

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Q: Rotate the curre about the X-axis. Find Hhe surface are a of the resulting Sur face.

A: Given: The curve y=13x3 over the interval 0,1, To determine: The surface area of the solid formed by…

Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = Vx, 3sy54

A: Given:y=x3  ,     3≤y≤4Surface area :S=∫ba2πx 1+dxdy2   dy

Q: The plane intersects the x-, y-, and z-axes in points P, Q, and R. Find the area of the triangle…

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Q: Sketch and identify the surface given by the equation Z=: x² +

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Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. x3/2, 0sxs 21 y

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Q: Shetch the region in the plane consisting of points whose polar coordinates satsfy the given…

A: Shaded area is the required area

Q: Each image shows a quadrilateral in a plane. The quadrilateral has been dilated using a center above…

A: Given the dilations and scale factors

Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = x2 - 1 -…

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Q: Consider curve C which is the intersection of the surfaces shown in the attached figure. image 1…

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Q: In the figure PQSO, is a trapezium in which PQ || OS, ZPOS = 135° and ZOSQ = 90° points P, Q and R…

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Q: Identify the surface in Cartesian coordinate for each of the following equations. a) p=5 and b)…

A: Given equations are in polar coordinates and we have to write their equation in Cartesian…

Q: Identify the given radius if the center lies at the origin. a. x2 + y2 = 15, 129 b. x2 + y2 = 121 с.…

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Q: Find the points on the surface y? = 81+ xz that are closest to the origin.

A: Distance formula is                   d2=x2+y2+z2                  d2=f=x2+81+xz+z2 Since,…

Q: the polar coordinates to find the volume of a sphere of radius 1. -

A: Given;  Sphere of radius 1.

Q: The line segment x = p - y,0 <y < p, is revolved about the y-axis to generate the cone as shown in…

A: Use simple integration formula for lateral surface area.

Q: A solid has circular base of radius 20 cm. Find the volume of the solid if every plane section…

A: Given: The base of solid: Circle with radius, r = 20 cmTo find; Volume of solid (V) for every plane…

Q: The curve y= 7,0 <x <3; is rotated about the x-axis. Find the exact area of the 3 resulting surface.

A: Given: The curve is Interval is from 0  to 3  and it is rotated about x axis

Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = 0SxS 12

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Q: ind the exact area of the surface obtained bY rotaing -- 2)2, 2sys3

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Q: Identify and sketch the surfaces described by the given equations. Explain.

A: The given equation is the y^2 + z^2=1

Q: A cone is cut along the shaded plane shown.  If the plane in the figure is perpendicular to the base…

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Q: Problem the circle xây? a? otatad about the x- escis, fnd the Jolume of the Solid geverated 2.

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Q: Identify the surface defined by the following equation. 2 y 3 15 The surface defined by the equation…

A: Topic = Geometry

Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. 1 In(x), 4< x <…

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Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = ? - Incx),…

A: Given that: y=14x2-12ln(x),     2≤x≤5

Q: The four views (front, side, top, orthogonal) of a surface are shown below. Which among the choices…

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Q: Given , x=4cos3θ and y=4sin3θ, 0<θ< π/2 (that is 0 is less than or equal to θ (theta) which is…

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Q: Identify and sketch the section of the surface at x = 0. 1 Туре: 61 61 61 61 4. 4 4. 4- 2 -8 -6 -4 4…

A: Let's find.

Q: Given that two curves can be constructed using the following equations y = x' and y = x* By using…

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Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. x = Va? - y²,…

A: We are given the equation of the surface as x=a2-y2, 0≤y≤a3. We need to find the area of the above…

Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. = Vx, 1sys 5

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Q: The line segment x = 1 - y, 0 ≤ y ≤ 1 is revolved about the y-axis. Find the surface area of the…

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Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = =x² - 1 1,2…

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Q: Pmblen #5. Given: dic radi ua = 6250 meters. 20 me tus. Sr we for : Surface are a of

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

Q: The circle x² + (y - 1)² = 1 is rotated about the line y = x - 5. A torus is obtained from this…

A: Given: The equation of circle is x2+y-12=1. Also, the given equation of line is y=x-5. The circle…

Q: rea of the closed region det

A: Given, the equation of the circle is                                        (x+2)2+(y-3)2=4

Q: Consider a Möbius strip cut along the dashed blue lines as shown below. What is the resulting…

A: When a mobius strip cut along these lines we get ,

Q: Identify the type of surface represented by the given equation. x? y? ? O Hyperboloid of two sheets…

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Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = 5 - x2,…

A: For the given curve- y=5-x2,              0≤x≤2 Surface area is given by- A=2π∫cdfy1+f'y2dy when it…

Q: Find the equation and sketch the graph of the surface generated by S revolved about the y-axis.

A: We are asked to find the equation of the surface generated by S revolved about the y-axis. The…

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.