Let be the region bounded on the left by the right branch of the hyperbola 2- = 1, on the right by the line a = 3 and below by the a-axis. Find the volume of the solid generated by revolving 2 about the line line a =-2 using shell method. Select one: 1)dy O Nane of these

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A: 1. The required region is bounded by the curves y=x+2and y=x2 , the axis of revolution is x axis.

Q: Find the volum e the solid in The first octant in side The para boloid 2-22-y%=0 and below the…

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Q: find the volume in the first octant under the plane z=y and inside the cylinder y²=4-x.

A: Given that, the cylinder is y2=4-x and the plane is z=y. y2=4-xy=±4-x Note that, the volume is in…

Q: (a) Between 1 and the disk x²+ (1+x² +y*) (b) Between % = 1 and the entire xy-plane. (1+x* + y?)*

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Q: QI) Find the volume of the solid generated by revolving region bounded by the curve (x-Jy)& the…

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Q: Find the volume of the solid that lies under the paraboloid z = x 2 + y 2 above the -plane, and…

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Q: Find the volume of the solid bounded by the paraboloid z = 4 + 4x² + 3y², the planes x = 2 and y =…

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A: Introduction: A solid of revolution is a solid figure formed by rotating a plane curve around a…

Q: solid generated by revolving the region bounded by the graphs of the equations about the x-axis.   y…

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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.