2. For the volume generated by rotating the region bounded by y = Vx,X-axis and x = 1 about the line y = 2, a) find it by the washer or shell method. b) Write the integral for same volume using the method you didn't use in part a)

Q: Find the volume of tetrahedron with vertices (0,0,0),(1,0,0),(0,1,0)and (0,0,2) by triple integral?…

A: We have to find the volume of the tetrahedrane with vertices 0,0,0, 1,0,0, 0,1,0 and 0,0,2 by triple…

Q: Find the volume generated by revolving the region bounded by y=−x^4+3x^3, y=0  revolving about the x…

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Q: Set up the integral to find the volume of the solid obtained when rotating the regionbounded by…

A: Given: y = x3,  x =0,  y=2,  y = 11 To set up: The integral to find the volume of the solid obtained…

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A: Volume

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A: The volume of Revolution about x -axis is given by  V = ∫x=ax =b π y2 dx  Given,  y = x32  x = 4 and…

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A: Here we use basic definition of volume .

Q: 5. Set up the integral to find the volume of the solid whose horizontal base is a circle of radius 2…

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Q: Find the volume produced by rotating the bounded region around the line y = 3 in the first quadrant…

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Q: Find the volume of the solid whose base is bounded by the circle x2 + y2 = 16 and whose cross…

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Q: Find the volume generated by revolving the area 1 bounded by y -, x = 2, x = 4, and y = 0 about the…

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Q: Find the volume of the solid obtained by rotating the area bounded by y = x^3, y = 0, and x = 1…

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Q: Find the volume of the solid of revolution formed by rotating each bounded region about the x-axis.…

A: Given:        f(x) = 1 - x ; x = 0 , y = 0    To find the volume of the solid of revolution…

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Q: If the path defined by z(x) from points C to W were rotated about the x-axis, what would be the…

A: Given zx=-0.00001x6+0.00026x-0.00313x4+0.01704x3-0.01298x2-0.30265x+3.56157 To find the volume of…

Q: What is the volume in the first octant bounded by x² + y – 4 = 0 and z = x. Use a triangular…

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Q: Find the volume generated by revolving the area 1 bounded by y = 2, x = 5, and y = 0 about the…

A: Given that to find the volume generated by revolving the area bounded by  y=1x3+17x2+72x,  x=2,…

Q: A hole of radius is bored through a cylinder of radius R>rat right angles to the axis of the…

A: A hole of radius is bored through a cylinder of radius R>rat right angles to the axis of the…

Q: Use triple integral to show that the volume of a sphere with radius 'a' ra". is

A: We have to use triple integral to show that volume of sphere with radius ' a ' is 43π a3. Equation…

Q: 1) Compute the volume of the solid obtained by revolving around the r-axis by 27 (ie. a full…

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

Q: The volume of the solid obtained by rotating the region enclosed by y = x", y = 6x, about the line y…

A: First sketch the curves then use method of disc to get the volume of solid obtained.

Q: 4. Compute the volume rotating the area shown through one revolution about the x-axis. generated by

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Q: Find the volumes of the solids whose bases are bounded by the circle x^2+y^2=4, with the indicated…

A: Given, x2+y2=4 Part a: We have, x2+y2=4⇒y2=-x2+4⇒y=±4-x2 Now we find the area to use in finding the…

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Q: The volume of the solid obtained by rotating the region enclosed by y=x3, y=16x, x≥0   about the…

A: to calculate the required volume of revolution

Q: Use the disk/washer method to set up a definite integral (set up only, do not evaluate the integral)…

A: Given :x=2yx=0y=9rotate about x=7 Formula used: V=∫cdπR2-r2dy

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Q: 4) By using the double integral, find the volume of the tetrahedron bounded by the 3x coordinate…

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Q: 2 Eualuate the inteyral 22 -- taken. throughout the volume • f sphere

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Q: Area bounded by y2 = x and x – y – 2 = 0, revolve about x = -1

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Q: Calculate the volume of the solid bounded inferiorly by the sphere (image 1) and superiorly by the…

A: Let, E be the region bounded below by the sphere x2+y2+z2=2z and bounded above by the cone z=x2+y2

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Q: use a theorem of Pappus to find the volume generated by revolving about the line x = 5 the…

A: “Pappus’s theorem for volumes:

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A: here is the solution

Q: . Find the volume bounded by z = 9 –x² – y² and z = 0. Give a numerical %3D answer.

A: Given that the region is bounded by z=9-x2-y2 and z=0. We know that the volume bounded between…

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A: We have to find the volume of the region.

Q: find the volume generated by revolving the area bounded by y = x^2 - 2x + 3 and y = 3 about the line…

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Q: Find the volume generated by revolving the area bounded by : 2, x = 5, and Ж — x3 + 9x² + 18x y = 0…

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Q: 2. Find the volume generated by revolving the area bounded by the parabola y² = 8x and its latus…

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Q: Find the volume of the solid formed by revolving the region bounded by the graphs of y = x² +1, y =…

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Q: Use double integral to find the volume of a tetrahedron bounded by the plane: 2x + y + z = 2 and 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.