The closed curve x²+y²-14x-14y+49=0 revolves about the line x=-3. Determine the volume generated.

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Q: Find the volume of the solid generated by revolving by the curve y = v2 – x² and x-axis: حد د واحدا…

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Q: Q2) Find the volume of the solid generated by revolving the 3x4 and the lines region bounded by the…

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Q: Find the center of mass of a thin plate of density δ = 3 bounded by the lines x = 0, y = x, and the…

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Q: Find the volume of the solid that results when the region enclosed by x = - y² + 7, and x = y + 4 is…

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Q: Q4) Fid the volume of the solid generated by revolving the region between the curve y = x + 1 and…

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Q: A container with a height of 3/2 is made by rotating the curve y = 3/2x^2, Osx<1, about the axis x =…

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Q: A thin plate of constant density k, bounded by the parabola y=3x² and the line y=3 has a mass 4k.…

A: If mass of a region R bounded between y=f(x) and y=g(x) from x=a  to x=b  Then there two moments,…

Q: Evaluate the volume of the surface of the shaped recreated by revolving the line y = 1/x as x goes…

A: Solution is written in below steps.

Q: Find the center of mass of a thin plate covering the region bounded below by the parabola y = x2 and…

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

A: We want to find the area bounded by the parabola y2 = 9x and the line y = 3x about the y-axis.

Q: Find the volume generated by the rotation of the region defined by the curve x=y2 and the line y=x-2…

A: Given curve x=y2 and the line y=x-2. Around the line y=-1. The objective is to find the volume…

Q: Find the volume of solid generated by revolving the region bounded by the curve y-4/x' and the lines…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r=2θ, 0≤θ≤4.5…

A: Given that  r=2θ, 0≤θ≤4.5 To Find the area enclosed by the closed curve obtained by joiningthe ends…

Q: Compute the volume of the solid obtained by revolving the graph of the function f(x) = 6x^5 on the…

A: Given fx=6x5 rotated about x axis in the interval x=-2 , x=+2Find volume generated .

Q: Find the volume of the solid form by the region bounded by the lines y = 16 – x, y = 3x + 12, and x…

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Q: Find the volume of the solid formed by revolving the curve defined by 9x²+4y²=36 about the line…

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Q: The area enclosed by y = 4x - x^2 and 2y = 2x + x^2 is revolved about the line x = -1. Using a…

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Q: Compute for the volume of the solid formed bounded by the equations (y- 4)2 = x - 3, x-10, y-4, and…

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Q: Consider a thin plate of constant density d lying in the regionbounded by the graphs of y = √x and x…

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Q: Find the volume of the solid generated by revolving about the line x = -4 the region bounded by the…

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Q: Find the volume of the solid generated byrevolving the region in the first quadrant bounded by the…

A: Using Shell Method:             2π∫01x.e-x dx Limits come from where the column can be created. (in…

Q: Find the volume of the solid generated by the region bounded by -x + y² = 8, x = -2y and y = -2…

A: Given , -x+y2=8, x=-2y, y=-2, revolved about x=-10. Find the volume of the solid generated by the…

Q: The region bounded by the curves y = x² – 2x and y = 4x is revolved about the line y = -1. Which…

A: The given curve is y=x2-2x and y=4x. Now, find the intersection point of these two curves.…

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 volume y=3x^2, x=1, and y=0 about x axis

A: y=3x^2, x=1, and y=0 about x axis

Q: find the volume of solid generated when the regions enclosed between the curves y=x^2 and x=y^2 is…

A: Given curves, y=x2andx=y2 To find the volume of solid generated by these curves about x - axis.

Q: Find the volume of the solid generated by revolving the regionbounded by the parabola y = x2 and the…

A: Given parabola y=x2 and the line y=1 about the line y=2limits of integration are x=-1 to x=1radii of…

Q: Compute the volume of the solid obtained by revolving the graph of the function f(x)=8x$ on the…

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Q: Find the center of mass of a thin plate covering the region bounded below by the parabola y = x 2…

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Q: Find the volume of the solid generated by revolving about the line y = -3 the region bounded by the…

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

Q: Find the volume of the solid of revolution when the curve y = x³ +1 is revolved around the x-axis on…

A: The given curve is y=x3+1 To find the volume of the solid revolution when the curve y=x3+1 is…

Q: Find the volume of the solid obtained when the region enclosed by the curve x=2-y² and find the x=y…

A: Draw the sketch of the given curve and lines.

Q: The volume of the solid generated when the region at the first quadrant bounded by the curve y = x²…

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Q: Find the volume generated by revolving about the line x - 4 = 0 the area bounded by the curve x2 =…

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Q: Compute the volume of the solid obtained by revolving the graph of the function f(x)= 9x5 on the…

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Q: Compute the volume of the solid obtained by revolving the graph of the function f(x) = 8x³ on the…

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Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

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Q: Find the volume and the surface area that generated due to rotate the bounded area between the curve…

A: I use washer method to find volume about x axis

Q: Consider a thin plate of constant density d lying in the regionbounded by the graphs of y = √x and x…

A: First find the intersection points of the given curve, by equating the y of both curves…

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.