find the volume . The base of the solid is the region bounded by the parabola y2 = 4x and the line x = 1 in the xy-plane. Each cross-section perpendicular to the x-axis is an equilateral triangle with one edge in the plane. (The triangles all lie on the same side of the plane.)

Q: Find the volume of the largest rectangular box in the first octant with three faces in the…

A: We have to find the volume of the largest rectangular box in the first octant with three faces in…

Q: The square region with vertices (11,0), (22,11), (11,22), and (0,11) is revolved about the x-axis to…

A: Given: The square region with vertices , ,  and  is revolved around the -axis to generate a solid.To…

Q: Find the length of the curve: y = + [1,2]. 16 ) Find the area of the surface obtained by rotating…

A:

Q: Find the volume of the described solid. 7) The solid lies between planes perpendicular to the x-axis…

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

Q: Find the area of the surface. The part of the plane x + 2y + 3z = 1 that lies inside the cylinder x2…

A:

Q: A light bulb is designed by revolving the graph of y = the surface area of the bulb and use the…

A:

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.