Find the volumes of the solids Find the volume of the solid generated by revolving the regionbounded by the parabola y2 = 4x and the line y = x about the line x = 4

Q: Find the volume of the cylindrical column standing on the area common to the parabolas x = y* , y =…

A: The given surface is z=12 + y - x2 and the given parabolas are  x = y2 , y = x2. The required volume…

Q: The base of a solid is the region bounded by the ellipse 4x +9y = 36. Find the volume of the solid…

A: a Given ellipse equation,4x2+9y2=36y2=4-49x2

Q: Find  the Volumeof the largest rectangular box lying above the xy-plane, with y less that or equal…

A: considerlength of rectangular box =x width of rectangular box  =yheight of rectangular box =z

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: Find the points on the surface y² = 16 + xz that are closest to the origin. smaller y-value (x, y,…

A:

Q: Find the volume of the region under the surface z = 9x5 and above the triangle in the xy-plane with…

A:

Q: Use polar coordinates to find the volume of the solid that lies below the paraboloid f(x,y) = 36-…

A:

Q: Find the volume of the solid bound by the surface z=(2x-y)^2+(x-y-1)^2 and the plane z=4. Question:…

A: Given that a solid is bounded by the surface and plane.

Q: Find the volume of the solid by subtracting two volumes. the solid enclosed by the parabolic…

A:

Q: Compute the volume of the column with a square base R= {(x,y): |x|< 3, |y| <3} cut by the plane z =…

A: We have to find volume whose base is square-

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.