Find the volumes of the solids generated by revolving the regions bounded by the lines and curves y = x², y = 0, x = 2 about the x-axis.

Q: y? = 4x, y = 2x - 4; about y-axis

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: Q1) Find the volume of the solid generated by revolving region bounded by the curve (y=x²+2) & the…

A: image is attached

Q: Find the volume of the solid bound between the paraboloid z = x^2 + y^2 and the plane x + z = 0 as…

A: Given data: The given equation of paraboloid is z=x2+y2. The equation of the plane is x+z=0. (a)…

Q: The region enclosed by the curves y = r³ and y = √√√ is rotated about the line z = 1. (a) Sketch and…

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Q: Find the volume generated by revolving bout the line y = -1 the area bounded by (х — 2)? 3D 4(у+ 2)…

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Q: Find the volumes of the solids generated by revolving the regions bounded by the graphs of the…

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Q: Calculate the coordinate ỹ and z of centroid for a U-shape drainage enclosed by surface z = y²,…

A: According to the given information, it is required to determine the coordinate of centroid for U…

Q: B) Find the solid volume obtained by rotating y = e-* , y = 1, x = 2 about y = 2

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Q: Find the volumes of the solids generated by revolving the region about the given line (a) y = x¹, y…

A: We will identify the region bounded  and then generate solid by revolving it about line x=-2 . To…

Q: Find the volume of the solid obtained by rotating the triangle (2,0)(2, 4)(1, 1) about the…

A: Solution :-

Q: Calculate the volume of the solid bounded by the sphere x2 + y2 +z2  =4 and the cylinder x2 + ( y -…

A: Triple integral is used to find the volume of a solid in three dimension. Sometimes, it is very…

Q: Find the volumes of the solids generated by revolving the regions bounded by the graphs of the given…

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

Q: Use the disk method or the shell method to find the volume of the solid generated by revolving the…

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

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.